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Represent Polygons on the Coordinate Plane

Graph polygons on coordinate grids and use coordinates to find side lengths, perimeter, and area.

6.GR.A.3 · Geometry & Coordinate Plane
Level
Guided practice with vocabulary support

🟠 Level 0 — Extra Support

Sentence starters: “First, I…” · “The answer is… because…” · “I know this because…”
W

Warm-Up

2 questions
Warm-Up 1
A rectangle has vertices at (1, 2), (5, 2), (5, 6), and (1, 6). What is the length of the bottom side?
Vocabulary: A vertex is a corner point. Vertices is the plural. The coordinate plane is a grid with an x-axis (horizontal) and y-axis (vertical).
Hint: The bottom side connects (1, 2) and (5, 2). Subtract the x-coordinates: 5 − 1 = ?
0 1 2 3 4 5 6 1 2 3 4 5 6 (1,2) (5,2) (5,6) (1,6)
✓Correct! The bottom side goes from x = 1 to x = 5. The length is 5 − 1 = 4 units.
✗Not quite. The bottom side connects (1, 2) and (5, 2). Since the y-values are the same, subtract the x-values: 5 − 1 = 4 units.
Warm-Up 2
True or False: You can find the perimeter of a polygon on a coordinate plane by adding all side lengths.
Vocabulary: The perimeter is the total distance around a shape. A polygon is a closed figure with straight sides.
✓Correct! Perimeter is the sum of all side lengths of a polygon.
✗Actually, this is true. Perimeter means the total distance around a polygon, found by adding all side lengths.
P

Practice

5 questions
Practice 1
A triangle has vertices at (0, 0), (6, 0), and (0, 4). Find the base, height, and area.
Vocabulary: The area of a shape is the space inside it, measured in square units.
Formula: Area of a triangle = ½ × base × height
Formula Card: Area of a triangle = ½ × base × height
0 1 2 3 4 5 6 1 2 3 4 (0,0) (6,0) (0,4)
Base = units
Height = units
Area = square units
Explain your reasoning:

Sentence frame: "The base is ___ units because I subtracted ___ from ___. The height is ___ units. The area is ½ × ___ × ___ = ___ square units."

✓All correct! Base = 6 (from x = 0 to x = 6), height = 4 (from y = 0 to y = 4), area = ½ × 6 × 4 = 12 square units.
✗Check your work. The base goes from (0, 0) to (6, 0) = 6 units. The height goes from (0, 0) to (0, 4) = 4 units. Area = ½ × 6 × 4 = 12 square units.
Practice 2
Look at the square on the coordinate grid below. What is its area?
Formula: Area of a square = side × side.
Hint: Find the length of one side by subtracting coordinates. Then multiply side × side.
Formula Card: Area of a square = side × side (s²)
-4 -3 -2 -1 1 2 3 4 1 2 3 4 -1 -2 -3 -4 (-2,-2) (2,-2) (2,2) (-2,2)
Explain your reasoning:
✓Correct! Each side is 2 − (−2) = 4 units. Area = 4 × 4 = 16 square units.
✗Find the side length first: from −2 to 2 is 4 units. Area = 4 × 4 = 16 square units (answer C).
Practice 3
Drag each set of vertices to its correct shape name.
Vocabulary: A rectangle has 4 right angles and opposite sides equal. A square has 4 equal sides and 4 right angles. A right triangle has one 90-degree angle. A parallelogram has two pairs of parallel sides.
(0,0), (6,0), (6,3), (0,3)
(1,1), (4,1), (4,4), (1,4)
(0,0), (5,0), (0,3)
(1,0), (4,0), (5,3), (2,3)
Rectangle
Square
Right Triangle
Parallelogram
✓All correct! You matched each set of vertices to the right shape.
✗Some matches are wrong. Check the side lengths and angles for each set of vertices. A square has 4 equal sides; a rectangle has opposite sides equal; a right triangle has 3 vertices with one 90-degree corner.
Practice 4
True or False: A rectangle with vertices (−1, 3), (4, 3), (4, −1), (−1, −1) has a perimeter of 18 units.
Strategy: Find each side length by subtracting coordinates. Add all four sides for the perimeter.
Hint: Width = 4 − (−1) = 5. Height = 3 − (−1) = 4. Perimeter = 2(5) + 2(4) = ?
Formula Card: Perimeter of a rectangle = 2 × length + 2 × width
-1 0 1 2 3 4 5 1 2 3 -1 -2 (-1,3) (4,3) (4,-1) (-1,-1)
Explain your reasoning:

Sentence frame: "The width is ___ units and the height is ___ units. The perimeter is ___ + ___ + ___ + ___ = ___ units."

✓Correct! Width = 5, height = 4. Perimeter = 5 + 4 + 5 + 4 = 18 units.
✗Let's check: width = 4 − (−1) = 5, height = 3 − (−1) = 4. Perimeter = 5 + 4 + 5 + 4 = 18. The statement is true.
Practice 5
Three vertices of a rectangle are (1, 1), (1, 5), and (7, 5). What is the missing vertex?
Strategy: A rectangle has 4 corners. The missing vertex must complete the shape. Look at which x and y values are needed.
Hint: You have x = 1 and x = 7. You have y = 1 and y = 5. Which combination is missing?
0 1 2 3 4 5 6 7 8 1 2 3 4 5 6 (1,1) (1,5) (7,5) ?
Explain your reasoning:

Sentence frame: "The missing vertex is (__, __) because the x-value must match ___ and the y-value must match ___."

✓Correct! The missing vertex is (7, 1). It shares x = 7 with (7, 5) and y = 1 with (1, 1).
✗The missing corner needs x = 7 (to align with the right side) and y = 1 (to align with the bottom). The answer is A: (7, 1).
★

Challenge

1 question
Challenge
Design a Garden! Plot a polygon with at least 4 vertices on the coordinate plane. List your vertices, then find the perimeter and area of your garden. Explain your strategy.
Tips: Use a simple shape like a rectangle or L-shape. Choose vertices with whole-number coordinates to make calculations easier.
Vocabulary: perimeter = distance around, area = space inside.
Formula Cards:
Area of a rectangle = length × width
Perimeter of a rectangle = 2(length) + 2(width)
Area of a triangle = ½ × base × height
Your vertices (list the ordered pairs):
Perimeter of your garden:
Area of your garden:
Explain your strategy for finding the perimeter and area:

Sentence frame: "My garden is a ___ with vertices at ___. I found each side length by subtracting coordinates. The perimeter is ___ units and the area is ___ square units."