Exercise 18 Page 410

When drawing the polygon, the first thing we should notice is its shape. This polygon has four vertices, so it is a quadrilateral. Let's draw it in a coordinate plane.

Notice that the sides of the quadrilateral are vertical lines and that the top and bottom are horizontal lines. Vertical and a horizontal lines are perpendicular to each other. This means that all of the angles in the polygon are right angles and that the quadrilateral is a rectangle. We can calculate its area using the formula for the area of a rectangle. A=l w In this formula, l is the length and w is the width. We can find the measure of the length and width using the Ruler Postulate. Let's start with NP.

NP=|x_2-x_1|

SubstituteII

x_1= - 2, x_2= 3

NP=| 3-( - 2)|

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Simplify right-hand side

SubNeg

a-(- b)=a+b

NP=|3 + 2|

AddTerms

Add terms

NP=|5|

AbsPos

|5|=5

NP=5

The length is 5 units. We will now find the width in the same way.

PQ=|y_2-y_1|

SubstituteII

y_1= 1, y_2= - 1

PQ=| - 1- 1|

▼

Simplify right-hand side

SubTerm

Subtract term

PQ=|- 2|

AbsNeg

|-2|=2

PQ=2

The width is 2 units. We can now calculate the area of the given rectangle. A=l w ⇒ 5* 2=10 square units