math class 678 4-in-1 skill sheets
6.G.A.3 6th Grade Geometry

Polygons & Quadrilaterals on the Coordinate Plane

Draw polygons in the coordinate plane given the coordinates of the vertices, and use coordinates to find the length of a side.

How to explain it

At this standard, students plot quadrilateral vertices on the coordinate plane, connect them to form quadrilaterals, and find horizontal and vertical side lengths using coordinate subtraction.

The anchor students hold onto: Horizontal side (same y): length = |x₂ − x₁|. Vertical side (same x): length = |y₂ − y₁|. Horizontal side (same y): length = |x₂ − x₁|. Vertical side (same x): length = |y₂ − y₁|.

Coordinate plane geometry connects to polygon side lengths in sheet #28 (6.G.A.3), real-world area problems (6.G.A.1), and extends through 7th-grade rational number work on four-quadrant planes.

Worked examples

Example 1
Draw rect ABCD; find perimeter.
Step 1AB: same y (y=1) → |6−1| = 5 units
Step 2BC: same x (x=6) → |4−1| = 3 units
Step 3P = 5 + 3 + 5 + 3 = 16 units
AnswerP = 16 units
Example 2
Find EF: E(2,6) and F(2,1).
Step 1Same x-coordinate (x = 2) → vertical side
Step 2EF = |6 − 1| = 5 units
AnswerEF = 5 units
Example 3
Find the two legs of △PQR.
Step 1P(0,0), Q(4,0), R(4,3) — plot and connect.
Step 2PQ: same y (y = 0) → horizontal: |4 − 0| = 4 units
Step 3QR: same x (x = 4) → vertical: |3 − 0| = 3 units
Step 4PR is diagonal — coordinate subtraction does not apply.
AnswerPQ = 4 units; QR = 3 units

Common mistakes

What students write Adding coordinates (x + y) or (x₂ + x₁) to find a side length.
The fix Side length uses subtraction: |x₂ − x₁| for horizontal or |y₂ − y₁| for vertical sides.
Try this A student found the perimeter of rectangle ABCD where A(1,2), B(5,2), C(5,6), D(1,6). Student's work: AB = |5 − 1| = 4 units BC = |6 − 2| = 4 units Perimeter = 4 + 4 = 8 units Find the error. Then find the correct perimeter.
What students write Computing the perimeter by adding only two sides of the quadrilateral.
The fix A quadrilateral has four sides. Add all four side lengths to find the perimeter.
Try this A student found the perimeter of hexagon ABCDEF where A(0,0), B(4,0), C(4,2), D(2,2), E(2,4), F(0,4). Student's work: AB = |4 − 0| = 4; BC = |2 − 0| = 2; CD = |4 − 2| = 2 DE = |4 − 2| = 2; EF = |2 − 0| = 2 Perimeter = 4 + 2 + 2 + 2 + 2 = 12 units Find the error. Then find the correct perimeter.
What students write Trying to find a diagonal side length by subtracting one pair of coordinates.
The fix Coordinate subtraction only works for H or V sides. A diagonal requires the Pythagorean theorem, which is a later skill.
What students write Counting only 4 sides on an L-shaped hexagon and missing 2 of the 6 sides.
The fix Trace around the polygon step by step. An L-shaped hexagon has 6 sides — list each one before adding.

Teacher tip

Head off the two predictable errors before they happen. First: Side length uses subtraction: |x₂ − x₁| for horizontal or |y₂ − y₁| for vertical sides. Second: A quadrilateral has four sides. Add all four side lengths to find the perimeter.