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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

4. Perimeter and Area in the Coordinate Plane

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Exercise 11 Page 410

Use the Distance Formula and the Ruler Postulate.

About22.43units

Practice makes perfect

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. Let's start with WU. We will use the Distance Formula to calculate its length.

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

SubstitutePoints

Substitute ( - 2,4) & ( 3,- 4)

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

a-(- b)=a+b

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

Add and subtract terms

WU=sqrt(5^2+(- 8)^2)

Calculate power

WU=sqrt(25+64)

Add terms

WU=sqrt(89)

Use a calculator

WU=9.43398...

Round to 2 decimal place(s)

WU≈ 9.43

We continue by calculating the length of the other two sides UV and VW. However, this time, we will use the Ruler Postulate.

Side	Coordinates	Ruler Postulate	Length
UV	( - 2,4) ( 3,4)	\| 3-( - 2)\|	5
VW	(3, 4) (3, - 4)	\| - 4- 4\|	8

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

P=UV+VW+WU

SubstituteValues

Substitute values

P≈ 5+8+9.43

Add terms

P≈ 22.43

The triangle's perimeter is approximately 22.43 units.

Subchapter links

Communicate Your Answer p.405

Monitoring Progress p.406-409

Exercises p.410-412