   Chapter 10.CR, Problem 37CR 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

Determine whether △ A B C , with vertices A 0 ,   0 ,   0 , B 1 ,   2 ,   4 , and C 0 ,   0 ,   8 , is an isosceles triangle.

To determine

Whether △ABC, with vertices A0, 0, 0, B1, 2, 4, and C0, 0, 8, is an isosceles triangle.

Explanation

The given vertices are A0, 0, 0, B1, 2, 4, and C0, 0, 8.

If the given vertices form a isosceles triangle, any two sides will be equal.

Let us find the distance AB.

x1,y1, z1=A0, 0, 0

x2,y2, z2=B1, 2, 4

Formula for distance between two points

d=x2-x12+y2-y12+z2-z12

Substituting the x and y co-ordinates

dAB=1-02+2-02+4-02

Simplifying,

dAB=12+22+42

Squaring,

dAB=1+4+16

dAB=21

Hence, dAB=P1P2=21

Let us find the distance BC

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