   Chapter 10.1, Problem 25E 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

Use the Distance Formula to determine the type of triangle that has these vertices:a) A ( 0, 0 ) ,   B ( 4 ,   0 ) , and C ( 2 ,   5 ) b) D ( 0, 0 ) ,   E ( 4 ,   0 ) , and F 2 ,   2 3 c) G ( - 5 ,   2 ) ,   H ( - 2 ,   6 ) , and K ( 2 ,   3 )

To determine

(a)

What type of triangle that has vertices A(0, 0), B(4, 0), and C(2, 5) using distance formula?

Explanation

Given vertices are,

A(0, 0), B(4, 0), and C(2, 5).

Sketch the vertices points in the graph as shown below,

Length of AB, BC and CA can be determined using distance formula,

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(4, 0)

Length of AB=(4-0)2+(0-0)2

Length of AB=(4)2

Length of AB=4

Coordinates of B(4, 0), and C(2, 5)

To determine

(b)

What type of triangle that has vertices D(0, 0), E(4, 0), and F2, 23 using distance formula?

To determine

(c)

What type of triangle that has vertices G(-5, 2), H(-2, 6), and K(2, 3) using distance formula?

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