Grade 6 Math · Topic 57

Polygons on the Coordinate Plane

Polygons can be drawn on the coordinate plane by plotting their vertices and connecting them in order. Distances along horizontal or vertical sides are easy to compute: just look at the difference of x-coordinates (horizontal) or y-coordinates (vertical).

Lesson alignment: 6.G.A.3 · Take your time. You can return to this lesson whenever you need it.

Explore visually

Find polygon measurements from coordinates

Plot each vertex, then use coordinate differences to find side lengths. Connect those lengths to a rectangle’s perimeter and area or a triangle’s area.

Think first: If two vertices share an x- or y-coordinate, how can their coordinates tell you the side length?

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Follow the worked examples

Read each step, then cover the explanation and see if you can explain why it works.

Worked example 1

Find the perimeter of a rectangle with vertices A(2,1), B(8,1), C(8,5), D(2,5).

Find the side lengths from the coordinate differences. Width = |8 - 2| = 6. Height = |5 - 1| = 4. Perimeter = 2(6 + 4) = 20 units.

Answer: P = 20 units

Worked example 2

Find the area of triangle with vertices (1,1), (7,1), (7,5).

Right triangle with legs |7-1| = 6 (horizontal) and |5-1| = 4 (vertical). A = 1/2(6)(4) = 12 sq units.

Answer: 12 sq units

Try a few on your own

Work these on paper first. Open “Check” when you are ready to compare your answer.

  1. Length from (2,3) to (9,3) =
    Check

    7

  2. Length from (4,-1) to (4,7) =
    Check

    8

  3. Length from (-3,5) to (6,5) =
    Check

    9

  4. Perim of rect: (0,0),(5,0),(5,3),(0,3)
    Check

    16

  5. Area of rect: (1,2),(8,2),(8,6),(1,6)
    Check

    28

  6. Area of right tri: (0,0),(6,0),(6,4)
    Check

    12

  7. Perim of sq: (2,2),(7,2),(7,7),(2,7)
    Check

    20

  8. Area of right tri: (1,1),(1,9),(5,1)
    Check

    16

Try this situation 1

A garden has corners at (1,2), (9,2), (9,6), (1,6). Find its area.

Show a worked solution

Answer: 32 sq units.

Find the side lengths from the coordinate differences. Width |9-1| = 8. Height |6-2| = 4. A = 8 × 4 = 32.

Try this situation 2

A triangular flag has vertices (0,0), (8,0), (0,5). Find its area.

Show a worked solution

Answer: 20 sq units.

Right triangle with legs 8 and 5. A = 1/2(8)(5) = 20.

Fresh questions · saved on this device

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10 question pool

Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.

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Check what you learned

Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.

1. A trapezoid has vertices at (1, 1), (7, 1), (8, 4), and (0, 4) on a coordinate plane. What is the area of this trapezoid in square units?

2. A triangle has vertices at (1, 2), (7, 2), and (7, 6) on a coordinate plane. What is the area of this triangle in square units?

3. A right triangle has vertices at (0, 0), (9, 0), and (0, 6) on a coordinate plane. Which expression can you use to find its area?

4. A composite shape is made by removing a right triangle from a rectangle. The rectangle has vertices at (0, 0), (5, 0), (5, 4), and (0, 4). The triangle has vertices at (5, 0), (5, 4), and (3, 0). What is the area of the remaining shape?

5. A trapezoid has vertices at (2, 3), (6, 3), (8, 7), and (3, 7) on a coordinate plane. Which method would determine its area most directly?

Practice and finish

Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.

Open the practice quiz

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More Grade 6 resources

Use these free materials if you want another explanation, extra paper practice, or a broader review.

Browse free Grade 6 topic lessons ↗Print Grade 6 worksheets ↗Review Grade 6 flashcards ↗Open the formula review ↗Try the Geometry: Area, Surface Area & Volume quiz ↗Try a full practice test ↗