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Elementary Geometry for College St...

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

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BuyFindarrow_forward

Elementary Geometry for College St...

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