Exercise 8 Page 34

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

We can see that the given figure is a square. Therefore, all the sides have equal lengths. QR = RS = ST = TQThe perimeter of a square can be expressed as shown below. P=4s In this formula s is the length of the side of the square. We can substitute the length of any of the four sides of the given square for s. Let's use QR. P=4QR This means that we only have to find the length of QR. We can use the Ruler Postulate to do this.

QR=|x_2 - x_1 |

SubstituteII

x_1= - 3, x_2= 1

QR=| 1-( - 3)|

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Simplify right-hand side

SubNeg

a-(- b)=a+b

QR=|1+3|

AddTerms

Add terms

QR=|4|

AbsPos

|4|=4

QR=4

Now, let's calculate the square's perimeter. We do so by substituting the value into the formula.

P=4QR

Substitute

QR= 4

P=4( 4)

Multiply

Multiply

P=16

The square's perimeter is 16 units.