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Chapter 1: Q. 126 (page 43)

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.

Short Answer

Expert verified

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

Step by step solution

01

Given information

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

02

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

We get

Slope=a-bb-a=-1

Therefore the slope is-1

03

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

Comparing the slope with standard equation, we get slope=1

And on multiplying both the slopes we get -1.

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

04

Find the midpoint of the points (a,b)(b,a)

We get,

M=(a+b2,b+a2)

And clearly this point lies ony=x

05

Conclusion

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

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Most popular questions from this chapter

Graph the line containing the point P and having slope m.

P(-1,3),m=0

Plot each pair of points and determine the slope of the line containing them. Graph the line by hand.

(-1,2);(-1,-2)

To solve an equation of the form {expression in x = 0}

using a graphing utility, we graph Y1= {expression in x}

and use ________ to determine each x-intercept of the

graph.

Find the length of the line segment. Assume that the endpoints of each line segment have integer coordinates.

Plot each pair of points and determine the slope of the line containing them. Graph the line by hand.

(4,2);(-5,2)
See all solutions

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