Skip to main content
Common Core Math6th GradeGeometry

6.G.3: Polygons in the Coordinate Plane

Also written as 6.G.A.3 and CCSS.MATH.CONTENT.6.G.A.3 · Cluster: Solve real-world and mathematical problems involving area, surface area, and volume.

Make Coordinate Grids for 6.G.3All 29 6th Grade Math Standards

The Official Wording

Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

Common Core State Standards, Grade 6, Geometry · Read it at the source · Checked October 14, 2026

What 6.G.3 Means in Plain English

Sixth graders plot corners like (−3, 2), (5, 2), (5, −4) and (−3, −4), join them into a rectangle, and read each side from the coordinates: the top runs from −3 to 5, so it is 8 units, and the right side from −4 to 2 is 6.

The number line has become a plane: the same subtraction that measures distance on one axis (6.NS.8) now gives side lengths, and 6.G.1 turns those into area. In 7th grade the drawings become scale drawings (7.G.1); in 8th, slanted sides get measured with the Pythagorean theorem (8.G.8).

6.G.3 I Can Statements

  • I can plot points in all four quadrants and connect them into a polygon.
  • I can find a side length by subtracting coordinates.
  • I can use the side lengths to find a perimeter or an area.

6.G.3 Worked Example

A school garden mapped on a grid with corners in three quadrants, measured by subtracting coordinates rather than counting squares.

Problem

A school maps its rectangular garden on a coordinate grid where 1 unit is 1 meter. The corners are (−3, 2), (5, 2), (5, −4) and (−3, −4). How long is each side, and what are the perimeter and area?

A garden with corners in three quadrants
  1. Plot the four points and connect them in order. Two points share y = 2 and two share y = −4: those pairs make the horizontal sides.(−3, 2), (5, 2), (5, −4), (−3, −4)
  2. A horizontal side has the same y, so its length is the distance between the x values. From −3 to 5 crosses 3 units to zero and 5 more.5 − (−3) = 8 m
  3. A vertical side has the same x, so subtract the y values. From −4 up to 2.2 − (−4) = 6 m
  4. With both side lengths known, the rectangle is ordinary 6.G.1 work.P = 2(8) + 2(6) = 28 m, A = 8 × 6 = 48 m²
AnswerSides of 8 m and 6 m, perimeter 28 m, area 48 m²

Check it: Count on the grid: from (−3, 2) to (5, 2) is 8 squares across, and from (5, 2) down to (5, −4) is 6 squares. The counts match the subtractions.

Common Mistakes with 6.G.3

Subtracting as if both coordinates were positive

From (−3, 2) to (5, 2): 5 − 3 = 2 units

Try this: Count the grid squares by hand: 3 to reach the y-axis, 5 more to reach x = 5, so the side is 8.

Swapping x and y when plotting

(−3, 2) plotted 2 to the left and 3 up

Try this: Plot with a finger: slide along the x-axis to the first number, then up or down to the second. The first number moves sideways.

Connecting the points in the wrong order

(−3, 2) joined to (5, −4), so the “rectangle” has an X through it

Try this: Connect the vertices in the order the problem lists them, and check that each side runs straight along a grid line before measuring.

Where 6.G.3 Fits

Comes Before5.G.1Plot points in the first quadrant and read their coordinates.5.G.2Solve real-world problems by graphing points in the first quadrant.
Alongside6.NS.8Graph in all four quadrants and find distances between points that share a coordinate.6.G.1Find the area of the polygon once its sides are known.
Comes Next7.G.1Work with scale drawings and compute actual lengths from them.8.G.8Find the distance between any two points with the Pythagorean theorem.

Practice 6.G.3

Graph Paper GeneratorFree ToolGrid paper for plotting vertices. A 1 cm square keeps points like (−3, 2) and (5, −4) far enough apart to label and count between.1 cm squaresFour quadrantsFull page
Make Graph Paper

Quick Check

  1. How far apart are (−6, 3) and (4, 3)?
  2. A square has vertices (1, 1), (1, 6), (6, 6) and (6, 1). What is its perimeter?
  3. Three vertices of a rectangle are (−2, −1), (−2, 5) and (3, 5). Find the fourth vertex and the area.

6.G.3: Other Names

6.G.36.G.A.3CCSS.MATH.CONTENT.6.G.A.3

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The explanation, I can statements, example, mistakes and practice on this page are EMStudio’s own, written beside the official wording. They are not part of the standard.