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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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Use slopes to decide whether the triangle with vertices at 6 ,   5 , - 3 ,   0 , and 4 ,   - 2 is a right triangle.

To determine

To check:

Whether the triangle with vertices at 6, 5, -3, 0, and 4, -2 is a right triangle.

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 A6, 5, B-3, 0, and C4, -2 be vertices of the triangle.

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

The given points are A6, 5 and B-3, 0.

Using the slope formula and choosing x1=6, x2=-3, y1=5, and y2=0.

mAB-=0-5-3-6

mAB-=-5-9

mAB-=59

The given points are B-3, 0 and C4, -2.

Using the slope formula and choosing x1=-3, x2=4, y1=0, and y2=-2

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