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Q. 126

Expert-verifiedFound in: Page 43

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

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 $y=x$

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

We get

Slope$=\frac{a-b}{b-a}\phantom{\rule{0ex}{0ex}}=-1$

Therefore the slope is $-1$

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 line $y=x$

We get,

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

And clearly this point lies on $y=x$

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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