   Chapter 10.2, Problem 36E 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

If A 2 ,   2 , B 7 ,   3 , and C 4 ,   x are the vertices of a right triangle with right angle C , find the value of x .

To determine

To find:

The value of x for the right triangle at C with vertices A2, 2, B7, 3, and C4, x.

Explanation

To check the triangle to be right triangle, we need to prove that any two lines are perpendicular to each other.

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 A2, 2, B7, 3, and C4, x be vertices of the right triangle.

The right angle is given at C.

Thus the line AC and BC are perpendicular to each other.

By finding the slopes of these lines, we can easily determine the value of x.

Let mBC-, and mAC- are the slopes of the line BC- and AC- respectively.

The given points are B7, 3 and C4, x.

Using the slope formula and choosing x1=7, x2=4, y1=3, and y2=x

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