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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 3 Page 408

Use the Distance Formula.

P ≈ 20.60 units

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 we can find 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 DE.

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

SubstitutePoints

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

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

a-(- b)=a+b

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

Add and subtract terms

DE=sqrt(7^2+0^2)

Calculate power

DE=sqrt(49)

Calculate root

DE=7

We continue by calculating the length of the other two sides EF and FD.

Side	Coordinates	sqrt((x_2-x_1)^2+(y_2-y_1)^2)	Length
EF	( 4,2) ( 4,- 3)	sqrt(( 4- 4)^2+( - 3- 2)^2)	5
FD	( 4,- 3) ( - 3,2)	sqrt(( - 3- 4)^2+( 2-( - 3))^2)	sqrt(74)

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

P=DE+EF+FD

SubstituteValues

Substitute values

P=7+5+sqrt(74)

Use a calculator

P= 20.60232...

Round to 2 decimal place(s)

P≈ 20.60

The perimeter of the triangle is approximately 20.60 units.

Subchapter links

Communicate Your Answer p.405

Monitoring Progress p.406-409

Exercises p.410-412