   Chapter 10.1, Problem 29E 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 two vertices of an equilateral triangle are at ( 0, 0 ) and ( 2 a ,   0 ) , what is the third vertex? To determine

What is the third vertex, if two vertices of an equilateral triangle are at (0, 0) and (2a, 0).

Explanation

Given vertices are,

(0, 0) and (2a, 0)

Given figure is,

Let the given triangle is ABC.

Length of AB =a

Coordinates of A=(0, 0)

Coordinates of B=(2a, 0)

Let the coordinates of C=(x, y)

Since, the given triangle is an equilateral, the length of three sides are equal.

AB=BC=CA=a

a can be determined using distance formula as below,

Distance Formula:

The distance between the two points (x1, y1) and (x2, y2) as below,

d=(x2-x1)2+(y2-y1)2

Coordinates of A(0, 0), B(2a, 0)

Length of MN=(2a-0)2+(0-0)2

Length of MN=(2a)2

Length of MN=2a

Coordinates of C can be determined from the length of AC and BC

A=(0, 0) and C=(x, y)

Length of AC=(x-0)2+(y-0)2

Length of AC=(x)2+(y)2=2a

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