Find the perimeter in the coordinate plane

In order to find the perimeter in the coordinate plane, you can use the ruler postulate and the distance formula.

Example #1

Find the perimeter of triangle ABC in the figure below

Perimeter in the coordinate plane

Find the length of each side of the triangle. Then, add the lengths to find the perimeter.

Using the ruler postulate, AB = |9 - 4| = |5| = 5

Using the ruler postulate, BC = |10 - -2| = |10 + 2| = |12| = 12

Using the distance formula, AC = √[(9 - 4)2 + (10 - -2)2]

AC = √[(5)2 + (10 + 2)2]

AC = √[(5)2 + (12)2]

AC = √[25 + 144]

AC = √[169]

AC = 13

AB + BC + AC = 5 + 12 + 13 = 17 + 13 = 30

The perimeter of triangle ABC is 30 units.

Example #2

Find the perimeter of trapezoid ABCD in the figure below

Perimeter in the coordinate plane

Find the length of each side of the trapezoid. Then, add the lengths to find the perimeter.

Using the ruler postulate, AB = |9 - -3| = |9 + 3| = |12| = 12

Using the ruler postulate, BC = |-3 - 3| = |-6| = 6

Using the ruler postulate, AD = |8 - -3| = |8 + 3| = |11| = 11

Using the distance formula, CD = √[(9 - -3)2 + (3 - 8)2]

CD = √[(9 + 3)2 + (-5)2]

CD = √[(12)2 + 25]

CD = √[144 + 25]

CD = √[169]

CD = 13

AB + BC + AD + CD = 12 + 6 + 11 + 13 = 18 + 24 = 42

The perimeter of trapezoid ABCD is 42 units.

Recent Articles

  1. Additive Inverse of a Complex Number

    Sep 24, 21 03:39 AM

    What is the additive inverse of a complex number? Definition and examples

    Read More

Enjoy this page? Please pay it forward. Here's how...

Would you prefer to share this page with others by linking to it?

  1. Click on the HTML link code below.
  2. Copy and paste it, adding a note of your own, into your blog, a Web page, forums, a blog comment, your Facebook account, or anywhere that someone would find this page valuable.