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Q.22

Expert-verified
Found in: Page 540

### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776

# Plot the points $A\left(6,3\right),\text{}B\left(-3,9\right),$ and $C\left(-3,-3\right)$ in a coordinate plane. Connect the points to form a triangle. Use the distance formula to find the side lengths. Then classify the triangle by its side lengths.

The side length measures are$10.82,\text{12},\text{10.82}$. The triangle is an isosceles triangle.

See the step by step solution

## Step 1. Given Information.

Points of each side is given as $A\left(6,3\right),\text{}B\left(-3,9\right),$ and$C\left(-3,-3\right)$.

## Step 2. Calculation.

Plot the points to form a triangle.

Distance between the two points $\left({x}_{1},{y}_{1}\right)$ and $\left({x}_{2},{y}_{2}\right)$ on a co-ordinate plane is given by the formula$\sqrt{{\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{1}\right)}^{2}}$.

Find the length of AB using the above formula.

$AB=\sqrt{{\left(-3-6\right)}^{2}+{\left(9-3\right)}^{2}}$

Subtract the numbers inside the bracket.

$AB=\sqrt{{\left(9\right)}^{2}+{\left(6\right)}^{2}}$

To find the square multiply each number with the same number.

$AB=\sqrt{81+36}$

$AB=\sqrt{117}$

The square root of 117 is approximately$10.82$.

So, side length of AB is$10.82$.

Find the length of BC using the distance formula.

$BC=\sqrt{{\left(-3-\left(-3\right)\right)}^{2}+{\left(-3-9\right)}^{2}}$

Now subtract the numbers inside the bracket.

$BC=\sqrt{{\left(0\right)}^{2}+{\left(12\right)}^{2}}$

To find the square multiply each number with the same number.

$BC=\sqrt{0+144}$

$BC=\sqrt{144}$

The square root of 114 is 12.

So, side length of BC is 12.

Find the length of CA using the distance formula.

$CA=\sqrt{{\left(-6-\left(-3\right)\right)}^{2}+{\left(-3-\left(-3\right)\right)}^{2}}$

Now subtract the numbers inside the bracket.

$CA=\sqrt{{\left(9\right)}^{2}+{\left(6\right)}^{2}}$

To find the square multiply each number with the same number.

$CA=\sqrt{81+36}$

$CA=\sqrt{117}$

The square root of 117 is approximately$10.82$.

So, the side length of CA is$10.82$.

## Step 3. Conclusion.

The side lengths of the triangle are $10.82,\text{}12,$ and$10.82$.

Since two sides are same the triangle formed is as isosceles triangle.

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