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Transformations

- Calculus
- Absolute Maxima and Minima
- Absolute and Conditional Convergence
- Accumulation Function
- Accumulation Problems
- Algebraic Functions
- Alternating Series
- Antiderivatives
- Application of Derivatives
- Approximating Areas
- Arc Length of a Curve
- Area Between Two Curves
- Arithmetic Series
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- Calculus of Parametric Curves
- Candidate Test
- Combining Differentiation Rules
- Combining Functions
- Continuity
- Continuity Over an Interval
- Convergence Tests
- Cost and Revenue
- Density and Center of Mass
- Derivative Functions
- Derivative of Exponential Function
- Derivative of Inverse Function
- Derivative of Logarithmic Functions
- Derivative of Trigonometric Functions
- Derivatives
- Derivatives and Continuity
- Derivatives and the Shape of a Graph
- Derivatives of Inverse Trigonometric Functions
- Derivatives of Polar Functions
- Derivatives of Sec, Csc and Cot
- Derivatives of Sin, Cos and Tan
- Determining Volumes by Slicing
- Direction Fields
- Disk Method
- Divergence Test
- Eliminating the Parameter
- Euler's Method
- Evaluating a Definite Integral
- Evaluation Theorem
- Exponential Functions
- Finding Limits
- Finding Limits of Specific Functions
- First Derivative Test
- Function Transformations
- General Solution of Differential Equation
- Geometric Series
- Growth Rate of Functions
- Higher-Order Derivatives
- Hydrostatic Pressure
- Hyperbolic Functions
- Implicit Differentiation Tangent Line
- Implicit Relations
- Improper Integrals
- Indefinite Integral
- Indeterminate Forms
- Initial Value Problem Differential Equations
- Integral Test
- Integrals of Exponential Functions
- Integrals of Motion
- Integrating Even and Odd Functions
- Integration Formula
- Integration Tables
- Integration Using Long Division
- Integration of Logarithmic Functions
- Integration using Inverse Trigonometric Functions
- Intermediate Value Theorem
- Inverse Trigonometric Functions
- Jump Discontinuity
- Lagrange Error Bound
- Limit Laws
- Limit of Vector Valued Function
- Limit of a Sequence
- Limits
- Limits at Infinity
- Limits at Infinity and Asymptotes
- Limits of a Function
- Linear Approximations and Differentials
- Linear Differential Equation
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- Logarithmic Differentiation
- Logarithmic Functions
- Logistic Differential Equation
- Maclaurin Series
- Manipulating Functions
- Maxima and Minima
- Maxima and Minima Problems
- Mean Value Theorem for Integrals
- Models for Population Growth
- Motion Along a Line
- Motion in Space
- Natural Logarithmic Function
- Net Change Theorem
- Newton's Method
- Nonhomogeneous Differential Equation
- One-Sided Limits
- Optimization Problems
- P Series
- Particle Model Motion
- Particular Solutions to Differential Equations
- Polar Coordinates
- Polar Coordinates Functions
- Polar Curves
- Population Change
- Power Series
- Radius of Convergence
- Ratio Test
- Removable Discontinuity
- Riemann Sum
- Rolle's Theorem
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- Second Derivative Test
- Separable Equations
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- Solutions to Differential Equations
- Surface Area of Revolution
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- The Fundamental Theorem of Calculus
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- The Power Rule
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- Theorems of Continuity
- Trigonometric Substitution
- Vector Valued Function
- Vectors in Calculus
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- Altitude
- Angles in Circles
- Arc Measures
- Area and Volume
- Area of Circles
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- Area of Parallelograms
- Area of Plane Figures
- Area of Rectangles
- Area of Regular Polygons
- Area of Rhombus
- Area of Trapezoid
- Area of a Kite
- Composition
- Congruence Transformations
- Congruent Triangles
- Convexity in Polygons
- Coordinate Systems
- Dilations
- Distance and Midpoints
- Equation of Circles
- Equilateral Triangles
- Figures
- Fundamentals of Geometry
- Geometric Inequalities
- Geometric Mean
- Geometric Probability
- Glide Reflections
- HL ASA and AAS
- Identity Map
- Inscribed Angles
- Isometry
- Isosceles Triangles
- Law of Cosines
- Law of Sines
- Linear Measure and Precision
- Median
- Parallel Lines Theorem
- Parallelograms
- Perpendicular Bisector
- Plane Geometry
- Polygons
- Projections
- Properties of Chords
- Proportionality Theorems
- Pythagoras Theorem
- Rectangle
- Reflection in Geometry
- Regular Polygon
- Rhombuses
- Right Triangles
- Rotations
- SSS and SAS
- Segment Length
- Similarity
- Similarity Transformations
- Special quadrilaterals
- Squares
- Surface Area of Cone
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- Surface Area of Sphere
- Surface Area of a Solid
- Surface of Pyramids
- Symmetry
- Translations
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- Triangle Inequalities
- Triangles
- Using Similar Polygons
- Vector Addition
- Vector Product
- Volume of Cone
- Volume of Cylinder
- Volume of Pyramid
- Volume of Solid
- Volume of Sphere
- Volume of prisms
- Mechanics Maths
- Acceleration and Time
- Acceleration and Velocity
- Angular Speed
- Assumptions
- Calculus Kinematics
- Coefficient of Friction
- Connected Particles
- Conservation of Mechanical Energy
- Constant Acceleration
- Constant Acceleration Equations
- Converting Units
- Elastic Strings and Springs
- Force as a Vector
- Kinematics
- Newton's First Law
- Newton's Law of Gravitation
- Newton's Second Law
- Newton's Third Law
- Power
- Projectiles
- Pulleys
- Resolving Forces
- Statics and Dynamics
- Tension in Strings
- Variable Acceleration
- Work Done by a Constant Force
- Probability and Statistics
- Bar Graphs
- Basic Probability
- Charts and Diagrams
- Conditional Probabilities
- Continuous and Discrete Data
- Frequency, Frequency Tables and Levels of Measurement
- Independent Events Probability
- Line Graphs
- Mean Median and Mode
- Mutually Exclusive Probabilities
- Probability Rules
- Probability of Combined Events
- Quartiles and Interquartile Range
- Systematic Listing
- Pure Maths
- ASA Theorem
- Absolute Value Equations and Inequalities
- Addition and Subtraction of Rational Expressions
- Addition, Subtraction, Multiplication and Division
- Algebra
- Algebraic Fractions
- Algebraic Notation
- Algebraic Representation
- Analyzing Graphs of Polynomials
- Angle Measure
- Angles
- Angles in Polygons
- Approximation and Estimation
- Area and Circumference of a Circle
- Area and Perimeter of Quadrilaterals
- Area of Triangles
- Argand Diagram
- Arithmetic Sequences
- Average Rate of Change
- Bijective Functions
- Binomial Expansion
- Binomial Theorem
- Chain Rule
- Circle Theorems
- Circles
- Circles Maths
- Combination of Functions
- Combinatorics
- Common Factors
- Common Multiples
- Completing the Square
- Completing the Squares
- Complex Numbers
- Composite Functions
- Composition of Functions
- Compound Interest
- Compound Units
- Conic Sections
- Construction and Loci
- Converting Metrics
- Convexity and Concavity
- Coordinate Geometry
- Coordinates in Four Quadrants
- Cubic Function Graph
- Cubic Polynomial Graphs
- Data transformations
- De Moivre's Theorem
- Deductive Reasoning
- Definite Integrals
- Deriving Equations
- Determinant of Inverse Matrix
- Determinants
- Differential Equations
- Differentiation
- Differentiation Rules
- Differentiation from First Principles
- Differentiation of Hyperbolic Functions
- Direct and Inverse proportions
- Disjoint and Overlapping Events
- Disproof by Counterexample
- Distance from a Point to a Line
- Divisibility Tests
- Double Angle and Half Angle Formulas
- Drawing Conclusions from Examples
- Ellipse
- Equation of Line in 3D
- Equation of a Perpendicular Bisector
- Equation of a circle
- Equations
- Equations and Identities
- Equations and Inequalities
- Estimation in Real Life
- Euclidean Algorithm
- Evaluating and Graphing Polynomials
- Even Functions
- Exponential Form of Complex Numbers
- Exponential Rules
- Exponentials and Logarithms
- Expression Math
- Expressions and Formulas
- Faces Edges and Vertices
- Factorials
- Factoring Polynomials
- Factoring Quadratic Equations
- Factorising expressions
- Factors
- Finding Maxima and Minima Using Derivatives
- Finding Rational Zeros
- Finding the Area
- Forms of Quadratic Functions
- Fractional Powers
- Fractional Ratio
- Fractions
- Fractions and Decimals
- Fractions and Factors
- Fractions in Expressions and Equations
- Fractions, Decimals and Percentages
- Function Basics
- Functional Analysis
- Functions
- Fundamental Counting Principle
- Fundamental Theorem of Algebra
- Generating Terms of a Sequence
- Geometric Sequence
- Gradient and Intercept
- Graphical Representation
- Graphing Rational Functions
- Graphing Trigonometric Functions
- Graphs
- Graphs and Differentiation
- Graphs of Common Functions
- Graphs of Exponents and Logarithms
- Graphs of Trigonometric Functions
- Greatest Common Divisor
- Growth and Decay
- Growth of Functions
- Highest Common Factor
- Hyperbolas
- Imaginary Unit and Polar Bijection
- Implicit differentiation
- Inductive Reasoning
- Inequalities Maths
- Infinite geometric series
- Injective functions
- Instantaneous Rate of Change
- Integers
- Integrating Polynomials
- Integrating Trig Functions
- Integrating e^x and 1/x
- Integration
- Integration Using Partial Fractions
- Integration by Parts
- Integration by Substitution
- Integration of Hyperbolic Functions
- Interest
- Inverse Hyperbolic Functions
- Inverse Matrices
- Inverse and Joint Variation
- Inverse functions
- Iterative Methods
- Law of Cosines in Algebra
- Law of Sines in Algebra
- Laws of Logs
- Limits of Accuracy
- Linear Expressions
- Linear Systems
- Linear Transformations of Matrices
- Location of Roots
- Logarithm Base
- Logic
- Lower and Upper Bounds
- Lowest Common Denominator
- Lowest Common Multiple
- Math formula
- Matrices
- Matrix Addition and Subtraction
- Matrix Determinant
- Matrix Multiplication
- Metric and Imperial Units
- Misleading Graphs
- Mixed Expressions
- Modulus Functions
- Modulus and Phase
- Multiples of Pi
- Multiplication and Division of Fractions
- Multiplicative Relationship
- Multiplying and Dividing Rational Expressions
- Natural Logarithm
- Natural Numbers
- Notation
- Number
- Number Line
- Number Systems
- Numerical Methods
- Odd functions
- Open Sentences and Identities
- Operation with Complex Numbers
- Operations with Decimals
- Operations with Matrices
- Operations with Polynomials
- Order of Operations
- Parabola
- Parallel Lines
- Parametric Differentiation
- Parametric Equations
- Parametric Integration
- Partial Fractions
- Pascal's Triangle
- Percentage
- Percentage Increase and Decrease
- Percentage as fraction or decimals
- Perimeter of a Triangle
- Permutations and Combinations
- Perpendicular Lines
- Points Lines and Planes
- Polynomial Graphs
- Polynomials
- Powers Roots And Radicals
- Powers and Exponents
- Powers and Roots
- Prime Factorization
- Prime Numbers
- Problem-solving Models and Strategies
- Product Rule
- Proof
- Proof and Mathematical Induction
- Proof by Contradiction
- Proof by Deduction
- Proof by Exhaustion
- Proof by Induction
- Properties of Exponents
- Proportion
- Proving an Identity
- Pythagorean Identities
- Quadratic Equations
- Quadratic Function Graphs
- Quadratic Graphs
- Quadratic functions
- Quadrilaterals
- Quotient Rule
- Radians
- Radical Functions
- Rates of Change
- Ratio
- Ratio Fractions
- Rational Exponents
- Rational Expressions
- Rational Functions
- Rational Numbers and Fractions
- Ratios as Fractions
- Real Numbers
- Reciprocal Graphs
- Recurrence Relation
- Recursion and Special Sequences
- Remainder and Factor Theorems
- Representation of Complex Numbers
- Rewriting Formulas and Equations
- Roots of Complex Numbers
- Roots of Polynomials
- Roots of Unity
- Rounding
- SAS Theorem
- SSS Theorem
- Scalar Triple Product
- Scale Drawings and Maps
- Scale Factors
- Scientific Notation
- Second Order Recurrence Relation
- Sector of a Circle
- Segment of a Circle
- Sequences
- Sequences and Series
- Series Maths
- Sets Math
- Similar Triangles
- Similar and Congruent Shapes
- Simple Interest
- Simplifying Fractions
- Simplifying Radicals
- Simultaneous Equations
- Sine and Cosine Rules
- Small Angle Approximation
- Solving Linear Equations
- Solving Linear Systems
- Solving Quadratic Equations
- Solving Radical Inequalities
- Solving Rational Equations
- Solving Simultaneous Equations Using Matrices
- Solving Systems of Inequalities
- Solving Trigonometric Equations
- Solving and Graphing Quadratic Equations
- Solving and Graphing Quadratic Inequalities
- Special Products
- Standard Form
- Standard Integrals
- Standard Unit
- Straight Line Graphs
- Substraction and addition of fractions
- Sum and Difference of Angles Formulas
- Sum of Natural Numbers
- Surds
- Surjective functions
- Tables and Graphs
- Tangent of a Circle
- The Quadratic Formula and the Discriminant
- Transformations
- Transformations of Graphs
- Translations of Trigonometric Functions
- Triangle Rules
- Triangle trigonometry
- Trigonometric Functions
- Trigonometric Functions of General Angles
- Trigonometric Identities
- Trigonometric Ratios
- Trigonometry
- Turning Points
- Types of Functions
- Types of Numbers
- Types of Triangles
- Unit Circle
- Units
- Variables in Algebra
- Vectors
- Verifying Trigonometric Identities
- Writing Equations
- Writing Linear Equations
- Statistics
- Bias in Experiments
- Binomial Distribution
- Binomial Hypothesis Test
- Bivariate Data
- Box Plots
- Categorical Data
- Categorical Variables
- Central Limit Theorem
- Chi Square Test for Goodness of Fit
- Chi Square Test for Homogeneity
- Chi Square Test for Independence
- Chi-Square Distribution
- Combining Random Variables
- Comparing Data
- Comparing Two Means Hypothesis Testing
- Conditional Probability
- Conducting a Study
- Conducting a Survey
- Conducting an Experiment
- Confidence Interval for Population Mean
- Confidence Interval for Population Proportion
- Confidence Interval for Slope of Regression Line
- Confidence Interval for the Difference of Two Means
- Confidence Intervals
- Correlation Math
- Cumulative Distribution Function
- Cumulative Frequency
- Data Analysis
- Data Interpretation
- Degrees of Freedom
- Discrete Random Variable
- Distributions
- Dot Plot
- Empirical Rule
- Errors in Hypothesis Testing
- Estimator Bias
- Events (Probability)
- Frequency Polygons
- Generalization and Conclusions
- Geometric Distribution
- Histograms
- Hypothesis Test for Correlation
- Hypothesis Test for Regression Slope
- Hypothesis Test of Two Population Proportions
- Hypothesis Testing
- Inference for Distributions of Categorical Data
- Inferences in Statistics
- Large Data Set
- Least Squares Linear Regression
- Linear Interpolation
- Linear Regression
- Measures of Central Tendency
- Methods of Data Collection
- Normal Distribution
- Normal Distribution Hypothesis Test
- Normal Distribution Percentile
- Paired T-Test
- Point Estimation
- Probability
- Probability Calculations
- Probability Density Function
- Probability Distribution
- Probability Generating Function
- Quantitative Variables
- Quartiles
- Random Variables
- Randomized Block Design
- Residual Sum of Squares
- Residuals
- Sample Mean
- Sample Proportion
- Sampling
- Sampling Distribution
- Scatter Graphs
- Single Variable Data
- Skewness
- Spearman's Rank Correlation Coefficient
- Standard Deviation
- Standard Error
- Standard Normal Distribution
- Statistical Graphs
- Statistical Measures
- Stem and Leaf Graph
- Sum of Independent Random Variables
- Survey Bias
- T-distribution
- Transforming Random Variables
- Tree Diagram
- Two Categorical Variables
- Two Quantitative Variables
- Type I Error
- Type II Error
- Types of Data in Statistics
- Variance for Binomial Distribution
- Venn Diagrams

Imagine you are lying in your bed and you see a fly enter your room and sit on the ceiling of your room. From time to time it moves from one place to another. How do you keep track of the locations of the fly?

Imagine another scenario, you are on a roller coaster and you go around in twists and turns. Are the actions taken by the fly on the ceiling and you on the roller coaster the same or are they different? How do we track the exact motions in these scenarios?

In this article, we will learn some **fundamental movements in two-dimensional space**. These are transformations and we will learn their definition, and types of transformations, and see examples.

**Transformations** are movements in space of an object.

We say a transformation is **rigid** if the object does not change its size or shape during the transformation. If the object changes its size during a transformation, then we call it a **non-rigid** transformation.

A rigid transformation does not change the size or shape of the object transformed. Examples of rigid transformations include:

**Translation**- moving of the shape, left, right, up or/and down;**Reflection**- reflecting a shape with respect to a line, the line could also be the x-axis or y-axis;**Rotation**- rotating a shape around a point, clockwise or anti-clockwise.

A non-rigid transformation can change the size or shape, or both size and shape, of the object. An example of a non-rigid transformation is **d****ilation **- blowing up or shrinking an object.

Translation can be thought of as the process of moving an object around in a graph sheet. For knowing the movement of an object we look at how its edge points are transformed.

The translation of a point (x, y) to a new point (x', y') can be understood from its **change** in the x and y coordinates. Under this transformation, the point has moved along the x-direction and along the y-direction.

Moreover,

a

**positive value in the x-direction**indicates the movement to the**right**and a**negative value**indicates movement to the**left**;

a

**positive value in the y-direction**indicates the movement**upwards**and the**negative value**indicates movement**downwards**.

If a is positive then you move right and if a is negative you move left.

If b is positive you move up and if b is negative you move down.

For example, translating the object by (2, −3) means that the x-coordinate of every point in an object will increase by two, and the y-coordinate of every point in an object will decrease by three. Successfully, the object will move two units to the right and three units downward.

Translate the given triangle ABC by (–7, –4).

**Solution**

Translate (–7, –4) means "move the given triangle to 7 units left and 4 units downwards". We can move the triangle if we move its edge points A(4, 6), B(1, 2), and C(5, 2).

Applying the translation to point A by moving 7 units left and 4 units down we have A'(–3, 2).

Similarly, we get on applying the translation to B and C the points B'(–6, –2) and C'(–2, –2). By joining A', B' and C' we have the translated triangle.

Translate the given hexagon ABCDEF by (–7, 7).

**Solution**

Translation by the vector (–7, 7) means we move the hexagon 7 units to the left and 7 units upwards.

To do this we apply the transformation to the edge points and join the translated points to obtain the hexagon A'B'C'D'E'F'.

A reflection can be thought of as seeing something through a mirror. So it is always with respect to a given line where the mirror is placed. The distance between the object and its image from the mirror is the same. Similar to translation to reflect an object you reflect the edge points of the object.

**Reflecting** **an object about a line **, means to move every point in the object at an equal distance to the other side of the line.

For example to reflect the point (1, 0) about the y-axis we first see the distance the point is from the y-axis. In this case, the point (1, 0) is 1 unit from the y-axis and so it will be 1 unit on the other side of the y-axis and so at (–1, 0).

Reflect shape A about the line . Label the resulting shape with the letter B.

**Solution**

To obtain the reflection we first draw the line of reflection . Then we move each corner of the shape the same distance from the line of reflection on the ‘other side'.

For example, the bottom left corner of A is the point (3, 1), which is 2 units from the line . On reflection, it will be 2 units on the other side of the line. So its reflection point is (–1, 1).

Notice there is no change in the y-coordinate of the point and its reflection. This is because the line of reflection is parallel to the y-axis. We do the same for all the edge points to obtain the reflected image.

Reflect shape A about the line (x-axis). Label the resulting shape with the letter A’.

**Solution**

Rotations are transformations where the object is rotated through some angles. Examples of rotations include the minute needle of a clock, merry-go-around, and so on.

In all cases of rotation, there will be a centre point which is not affected by the transformation. In the clock the point where the needle is fixed in the middle does not move at all. In other words, the needle rotates around the clock about this point.

**Rotating an object d ^{o }about a point (a, b)** is to rotate every point of the object such that the line joining the points in the object and the point (a, b) rotates at an angle d

If d is positive then it is clockwise, otherwise, it is anticlockwise. In both transformations, the size and shape of the figure stay exactly the same.

The general rule of transformation of rotation about the origin (0, 0) is as follows.

Type of Rotation | Original Points | Switched Points (Anticlockwise Rotation) | Switched Points (Clockwise Rotation) |

To rotate 90 ^{0} | (x, y) | (−y, x) | (y, −x) |

To rotate 180 ^{0} | (x, y) | (−x, −y) | (−x, −y) |

To rotate 270 ^{0} | (x, y) | (y, −x) | (−y, x) |

Rotate the given shape ABC, 90^{º} clockwise and anticlockwise about the origin.

Original Points(x, y) | Switched Points(anticlockwise rotation)(−y, x) | Switched Points (clockwise rotation)(y, −x) |

(−3, 5) | (−5, −3) | (5, 3) |

(−6, 2) | (−2, −6) | (2, 6) |

(−3, 2) | (−2, −3) | (2, 3) |

**Solution**

Rotate the given shape to 270^{º} clockwise and anticlockwise about the origin.

Original Points (x, y) | Switched Points(counter-clockwise rotation)(y, −x) | Switched Points(clockwise rotation)(−y, x) |

(−4, 6) | (6, 4) | (−6, −4) |

(−6, 4) | (4, 6) | (−4, −6) |

(−2, 4) | (4, 2) | (−4, −2) |

(−3, 1) | (1, 3) | (−1, −3) |

Dilation is a transformation, which is used to resize the object to be larger or smaller. This transformation produces an image that is the same as the original in shape, but there is a difference in the size of the object.

- If a dilation creates a larger image, then it is known as
**enlargement**(a stretch).

- If a dilation creates a smaller image, then it is known as
**reduction**(a shrink).

A description of a dilation includes the** ****scale factor** (or ratio) and the **centre of the dilation**.

**Dilating an object by a scale factor k and about the centre of dilation (a, b)** means to move every point in the object by the scale times the distance of the point from the centre of dilation.

- If the scale factor is greater than 1, the image is an enlargement (a stretch).

- If the scale factor is between 0 and 1, the image is a reduction (a shrink).

For the scale factor , and origin being the centre of dilation we have the rule

.

That is, the original point (x, y) is changed as (3x, 3y). In this case, the dilation image will be stretched.

For, we get

.

In this case, the dilation image will be shrunk.

Dilate the given shape A by a factor of 2 with the origin as the centre of dilation.

**Solution**

The edges of shape A have the coordinates (1, 1), (1, 3), (3, 0), and (3, 3).

Now the coordinates of the given shape are multiplied by 2. They are (2,2), (2,6), (6,0), (6,6).

The Original Shape A and the Enlarged Shape B are represented in the following diagram.

Dilate the given shape A by a factor of 0.5 with the origin as the fixed point.**Solution**

The edges of shape A have the coordinates (6, 6), (6, 2), and (4, 2).Now the coordinates of the given shape are multiplied by 0.5. We then get the new coordinates (3, 3), (3, 1), (2, 1).The Original Shape A and the Shrinked Shape B are represented in the following diagram.

The edges of shape A have the coordinates (6, 6), (6, 2), and (4, 2).Now the coordinates of the given shape are multiplied by 0.5. We then get the new coordinates (3, 3), (3, 1), (2, 1).The Original Shape A and the Shrinked Shape B are represented in the following diagram.

When an object undergoes more than one transformation sequentially we call it a composite transformation. For example, a triangle undergoing translation first followed by dilation. There can be two or more transformations done one after another.

Rotate the given shape A to 90^{º} counter-clockwise direction about the origin, then reflect the resultant shape about the line x = 0, and finally translate the resultant shape into (–1, 7).

Original Points (x, y) | Switched Points (counter-clockwise rotation) (−y, x) |

(–6, 2) | (–2, –6) |

(–3, 2) | (–2, –3) |

(–2, 5) | (–5, –2) |

(–4, 5) | (–5, –4) |

- Transformations are movements of objects in space.
**Rigid Transformations**do not change the size or shape of the object after transformation.- Examples of rigid transformations include translation, reflection and rotation.

- Examples of rigid transformations include translation, reflection and rotation.
**Non-Rigid Transformations**can change the size or shape, or both, of the object.- Dilation is an example of a non-rigid transformation.

**Translation**(sometimes called ‘movement’) is the process of moving something around.- To translate an object by a vector means to move every point in the object a units in the x-direction and b units in the y-direction.
- If a is positive then you move right and if a is negative you move left.
- If b is positive you move up and if b is negative you move down.

**Reflection**occurs when each point in the shape is reflected about a line of reflection.- After reflection, the image is at the same distance from the line as the pre-image but on the other side of the line.

**Rotation**rotates each point in the shape at a certain degree with respect to a point.- The shape rotates counter-clockwise when the degrees are positive;
- And rotates clockwise when the degrees are negative.

**Dilation**is a transformation which is used to resize an object, making it larger or smaller. A description of a dilation includes the scale factor (or ratio) and the centre of the dilation.

♦ If the scale factor is**greater than 1**, the image is an enlargement (a stretch).

♦ If the scale factor is**between 0 and 1**, the image is a reduction (a shrink).

Transformations are movements in space of an object.

A translation is an example of a transformation.

The five transformations are translation, reflection, rotation, dilation, and shear.

More about Transformations

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