   Chapter 10.CR, Problem 19CR 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

Show that the triangle whose vertices are A 3 ,   6 , B - 6 ,   4 , and C 1 ,   - 2 is an isosceles triangle.

To determine

To prove:

The triangle formed by the vertices A3, 6, B-6, 4, and C1, -2 is an isosceles triangle.

Explanation

Isosceles triangle have two equal sides called legs and the third side is called base.

We have to prove that the distance between any two sides are equal.

The given vertices are A3, 6, B-6, 4, and C1, -2

First find the distance between A and B.

x1,y1=A3, 6

x2,y2=B-6, 4

Formula for distance between two points

dAB-=x2-x12+y2-y12

Substituting the x and y co-ordinates

dAB-=-6-32+4-62

On solving this,

dAB-=-92+-22

Squaring,

dAB-=81+4

dAB-=85

Now, find the distance between B and C

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