Exercise 10 Page 34

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 finding 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 XY.

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

Substitute ( - 1,3) & ( 3,0)

XY=sqrt(( 3-( - 1))^2+( 0- 3)^2)

a-(- b)=a+b

XY=sqrt((3+1)^2+(0-3)^2)

Add and subtract terms

XY=sqrt(4^2+(- 3)^2)

Calculate power

XY=sqrt(16+9)

Add terms

XY=sqrt(25)

Calculate root

XY=5

We continue by calculating the length of the other two sides YZ and ZX.

Side	Coordinates	sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)	Length
YZ	( 3,0) ( - 1,- 2)	sqrt(( - 1- 3)^2 + ( - 2- 0)^2)	sqrt(20)
ZX	( - 1,- 2) ( - 1,3)	sqrt(( - 1-( - 1))^2 + ( 3-( - 2))^2)	5

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

P=XY+YZ+ZX

Substitute values

P=5+sqrt(20)+5

Use a calculator

P=14.47213...

Round to 2 decimal place(s)

P≈ 14.47

The triangle's perimeter is approximately 14.47 units.

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