   Chapter 10.CR, Problem 18CR 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 - 2 ,   - 3 , B 4 ,   5 , and C - 4 ,   1 is a right triangle.

To determine

To prove:

The triangle formed by the following vertices A-2, -3, B4, 5, and C-4, 1 is a right triangle.

Explanation

To prove ABC is a right triangle, we have to prove the following statement.

The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the triangle.

The given vertices are A-2, -3, B4, 5, and C-4, 1

Find the slope of AB.

x1,y1=A-2, -3

x2,y2=B4, 5

Formula for slope joining the line segment.

Slope is denoted by m.

m=y2-y1x2-x1

Here x1x2

Substituting the x and y co-ordinates.

mAB-=5--34--2

Simplifying,

mAB-=5+34+2

mAB-=86

Cancelling the common factors,

mAB-=43

Find the slope of BC.

x1,y1=B4, 5

x2,y2=C-4, 1

Substituting the x and y co-ordinates

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