Exercise 7 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 rectangle. Therefore, its perimeter can be expressed as shown below. P=2l +2wIn this formula l is the length of the longer side of the rectangle and w is the length of the shorter side of the rectangle. In our case l=GH=KJ and w=KG=JH. P=2GH+2KG This means that we only have to find GH and KG. We can use the Ruler Postulate to do this. Let's start with GH.

GH = |y_2 - y_1 |

SubstituteII

y_1= 4, y_2= - 3

GH=| - 3- 4|

SubTerm

Subtract term

GH=|- 7|

AbsNeg

|-7|=7

GH=7

We can calculate the length of KG in a similar way.

KG=| x_2 - x_1|

SubstituteII

x_1= - 2, x_2= 2

KG=| 2-( - 2)|

▼

Simplify right-hand side

SubNeg

a-(- b)=a+b

KG=|2+2|

AddTerms

Add terms

KG=|4|

AbsPos

|4|=4

KG=4

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

P=2GH+2KG

SubstituteII

GH= 7, KG= 4

P=2( 7)+2( 4)

Multiply

Multiply

P=14+8

AddTerms

Add terms

P=22

The rectangle's perimeter is 22 units.