   Chapter 8.1, Problem 9SWU ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# In Exercises 7–10, show that the points form the vertices of the indicated polygon.Right triangle: ( − 1 , 3 ) , ( 3 , 5 ) , ( 5 , 1 )

To determine

To prove: The provided points (1,3), (3,5) and (5,1) are the vertices of the right triangle.

Explanation

Given Information:

The provided vertices of polygon are (1,3), (3,5) and (5,1).

Formula used:

If sum of the square of the length of two sides of a polygon are equal to square of the length of third side of a polygon, then the polygon is known as right triangle.

a2+b2=c2

Here, a and b are the length of two sides of right triangle and c is the length of hypotenuse of right triangle.

Write the formula to find the distance between two points.

d=(x2x1)2+(y2y1)2

Here, (x1,y1) and (x2,y2) are the two points in coordinate system.

Proof:

Draw the diagram of polygon from the provided data,

From above diagram, calculate the distance between BC by use of distance formula,

a=(3(1))2+(53)2=(4)2+(2)2=16+4=20

Further solve the above equation,

a=25

From above diagram, calculate the distance between AC by use of distance formula,

b=(5

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