Exercise 15 Page 64

To determine the perimeter of the polygon, we must find the sum of its side lengths. This polygon has three vertices, so it is a triangle. Let's draw it in a coordinate plane.

Before we can find the sum of the side lengths, we must find the length of each side. We can use the Distance Formula to do this. Let's start with AB.

AB = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)

SubstitutePoints

Substitute ( 4,5) & ( -4,-1)

AB=sqrt(( 4-( -4))^2+( 5-( -1))^2)

SubNeg

a-(- b)=a+b

AB=sqrt((4+4)^2+(5+1)^2)

AddTerms

Add terms

AB=sqrt((8)^2+(6)^2)

CalcPow

Calculate power

AB=sqrt(64+36)

AddTerms

Add terms

AB=sqrt(100)

CalcRoot

Calculate root

AB=10

We continue by calculating the length of the other two sides, BC and CA.

Side	Coordinates	sqrt((x_2-x_1)^2+(y_2-y_1)^2)	Length
BC	( 4,5) ( 4,-2)	sqrt(( 4- 4)^2+( - 1- 5)^2)	7
CA	( 4,-2) ( - 4,-1)	sqrt(( - 4- 4)^2+( -1-( -2))^2)	sqrt(65)

Now, let's calculate the triangle's perimeter. We do so by adding the three sides.

P=AB+BC+CA

SubstituteValues

Substitute values

P=10+7+sqrt(65)

AddTerms

Add terms

P=17+sqrt(65)

The triangle's perimeter is approximately (17+sqrt(65)) units.