Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

Show that the line containing the points (a, b) and (b, a), a b, is perpendicular to the line y = x. Also show that the midpoint of (a, b) and (b, a) lies on the line y = x.

We show that the lines are perpendicular to line $y = x$ and also we show that the midpoints lie on the line $y = x$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

We are given that a line contains a point $(a, b), (b, a)$

Step 2: We find the slope of line containing points (a,b)(b,a)

We get

Slope $= \frac{a - b}{b - a} = - 1$

Therefore the slope is $- 1$

Step 3: We find the slope of line y=x and compare them

Comparing the slope with standard equation, we get $s l o p e = 1$

And on multiplying both the slopes we get $- 1$ .

Hence the line containing point $(a, b) (b, a)$ is perpendicular to line $y = x$

Step 4: Find the midpoint of the points (a,b)(b,a)

We get,

$M = (\frac{a + b}{2}, \frac{b + a}{2})$

And clearly this point lies on $y = x$

Step 5: Conclusion

We proved that the two lines are perpendicular and the midpoint of (a,b) (b,a) lie on the line $y = x$

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Show that the line containing the points (a, b) and (b, a), a b, is perpendicular to the line y = x. Also show that the midpoint of (a, b) and (b, a) lies on the line y = x.

Step by Step Solution

Step 1: Given information

Step 2: We find the slope of line containing points (a,b)(b,a)

Step 3: We find the slope of line y=x and compare them

Step 4: Find the midpoint of the points (a,b)(b,a)

Step 5: Conclusion

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Show that the line containing the points (a, b) and (b, a), a b, is perpendicular to the line y = x. Also show that the midpoint of (a, b) and (b, a) lies on the line y = x.

Step by Step Solution

Step 1: Given information

Step 2: We find the slope of line containing points (a,b)(b,a)

Step 3: We find the slope of line y=x and compare them

Step 4: Find the midpoint of the points (a,b)(b,a)

Step 5: Conclusion

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