Polygons on the coordinate plane worksheet

Grade 6 math, Common Core 6.G.A.3. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

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Polygons on the coordinate plane

Grade 6 math, Common Core 6.G.A.3

Use the coordinates to answer each question.

1.
Three corners of a rectangle are (−2, −2), (6, −2) and (6, 3). What is the fourth corner?
2.
A rectangle has vertices (−4, −7), (4, −7), (4, 0) and (−4, 0). Find its perimeter and area.
3.
How long is the side from (3, 3) to (3, 8)?
4.
A rectangle has vertices (−4, −3), (0, −3), (0, 4) and (−4, 4). Find its perimeter and area.
5.
Three corners of a rectangle are (1, −5), (6, −5) and (6, 3). What is the fourth corner?
6.
A right triangle has vertices (−5, −5), (−5, −2) and (4, −5). Find its area.
7.
Three corners of a rectangle are (−7, −5), (−1, −5) and (−1, 3). What is the fourth corner?
8.
A right triangle has vertices (−5, 1), (−5, 10) and (4, 1). Find its area.
9.
A right triangle has vertices (−7, −3), (−7, 5) and (2, −3). Find its area.
10.
A rectangle has vertices (1, −2), (4, −2), (4, 4) and (1, 4). Find its perimeter and area.

Answer key: Polygons on the coordinate plane

Grade 6 math. Each answer has a few worked steps, to help check the method as well as the answer.

1. (−2, 3)
It lines up with (−2, −2) and (6, 3)
2. Perimeter 30 units, area 56 square units
Width: 4 − (−4) = 8Height: 0 − (−7) = 7
3. 5 units
Same x, so 8 − 3 = 5
4. Perimeter 22 units, area 28 square units
Width: 0 − (−4) = 4Height: 4 − (−3) = 7
5. (1, 3)
It lines up with (1, −5) and (6, 3)
6. 13.5 square units
Legs: 3 and 912 × 9 × 3 = 13.5
7. (−7, 3)
It lines up with (−7, −5) and (−1, 3)
8. 40.5 square units
Legs: 9 and 912 × 9 × 9 = 40.5
9. 36 square units
Legs: 8 and 912 × 9 × 8 = 36
10. Perimeter 18 units, area 18 square units
Width: 4 − 1 = 3Height: 4 − (−2) = 6

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About polygons on the coordinate plane

When two corners of a shape share an x-coordinate or a y-coordinate, the side between them is vertical or horizontal, and its length is the difference of the other coordinates. That lets you find perimeter and area straight from the coordinates, without drawing.

Worked example 1

A rectangle has vertices (0, −4), (2, −4), (2, 1) and (0, 1). Find its perimeter and area.

Step 1.Width: 2 − 0 = 2
Step 2.Height: 1 − (−4) = 5

Answer: Perimeter 14 units, area 10 square units

Worked example 2

Three corners of a rectangle are (−7, −7), (−2, −7) and (−2, 2). What is the fourth corner?

Step 1.It lines up with (−7, −7) and (−2, 2)

Answer: (−7, 2)

Worked example 3

A right triangle has vertices (−5, 1), (−5, 4) and (1, 1). Find its area.

Step 1.Legs: 3 and 6
Step 2.12 × 6 × 3 = 9

Answer: 9 square units

Watch out for

Same x-value: subtract the y-values. Same y-value: subtract the x-values.
If one coordinate is negative and the other positive, add their distances from 0.
Sketch the points quickly to see which corners are next to each other.

Practice polygons on the coordinate plane online

On StudyWiz, your kid can practice polygons on the coordinate plane with 5-question quizzes that are checked as they go, with an explanation for every answer. When a homework problem is the trouble, Wiz gives a hint for each step instead of the answer.

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