   Chapter 10.2, Problem 27E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Find x such that the line through 2 ,   - 3 and 3 ,   2 is perpendicular to the line through - 2 ,   4 and x ,   - 1 .

To determine

To find:

The value of x for the line containing the points 2, -3 and 3, 2 is perpendicular to the line containing the points -2, 4 and x, -1.

Explanation

By theorem,

If two lines are perpendicular, then the product of their slopes is -1 or one slope is negative reciprocal of the other slope.

(i.e) If l1l2, then m1.m2=-1 or m2=-1m1

The slope of the line that contains the points x1,y1 and x2,y2 is given by

m=y2-y1x2-x1 for x2x1

Let the slope of the line containing the points 2, -3 and 3, 2 be denoted as m1.

Using the slope formula and choosing x1=2, x2=3, y1=-3, and y2=2

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