Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.GR.3

Lesson 7.7Represent Polygons on the Coordinate Plane

Set B · Version ASecond form · supported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can draw polygons from their vertex coordinates on the coordinate plane, and use coordinates to find side lengths and solve perimeter and area problems.

Why This Matters A polygon's vertices are given as coordinates: (-4.5, 3), (5, 3), (5, -3.75), and (-4.5, -3.75). What is its perimeter?

RememberRepresent Polygons on the Coordinate Plane

Polygons on the Coordinate Plane Graph the points, connect them in order, and the polygon appears. Then the same coordinates that placed the corners tell you exactly how long each side is.

  1. Plot all given vertices and connect them in order to form the polygon.
  2. Find side lengths by counting grid units or using coordinate distance formulas.
  3. Perimeter = Sum of all side lengths; Area = Use standard polygon formulas

Words: vertex (vértice)polygon (polígono)perimeter (perímetro)distance between vertices (distancia entre vértices)scale (escala)

Part 1Understand the ideamodels and meaning
  1. 1Write the name of the correct group on each line.

    Sort each pair of vertices by the kind of side it makes.

    Groups: Vertical side (same x) Horizontal side (same y)
    • (5, 3) and (5, −3)
    • (−2, 1) and (−2, 6)
    • (4, −1) and (4, 7)
    • (−4, 3) and (5, 3)
    • (0, −2) and (6, −2)
    • (−3, 5) and (2, 5)

    Hint Look at which coordinate REPEATS in the pair — that is the direction that does not change.

  2. 2Complete the table. Show how you found each value.

    Find the distance between each pair of vertices.

    VerticesShared coordinateDistance (units)
    (−4, 3) and (5, 3)
    (5, 3) and (5, −4)
    (−2, −1) and (6, −1)

    Hint Distance across zero adds the two distances from the axis: from −4 to 5 is 4 + 5.

    Show your work
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    Vertices (−2, 6) and (−2, −6): the distance between them is

    1. A0 units
    2. B4 units
    3. C12 units
    4. D36 units

    Hint Which coordinate differs?

    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    What is the distance between (−5, 2) and (3, 2)?

    1. A2 units
    2. B8 units
    3. C−8 units
    4. D15 units
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    What is the horizontal distance between (−4, 5) and (2, 5)?

    1. A2
    2. B−2
    3. C6
    4. D−6
    Show your work
  4. 6Circle the letter of the best answer. Show how you know.

    What is the vertical distance between (3, −2) and (3, 6)?

    1. A3
    2. B4
    3. C8
    4. D−8
    Show your work

Explain your thinkingTake a side you both put under 'Slanted.' Why does subtracting coordinates give the wrong length there, and what has to be true about two vertices for subtraction to work?

Sentence starter Subtracting works when the two vertices share ___, so for ___ I cannot ___.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.GR.3

Lesson 7.7Represent Polygons on the Coordinate Plane

Set B · Version BSecond form · core practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can draw polygons from their vertex coordinates on the coordinate plane, and use coordinates to find side lengths and solve perimeter and area problems.

Why This Matters A polygon's vertices are given as coordinates: (-4.5, 3), (5, 3), (5, -3.75), and (-4.5, -3.75). What is its perimeter?

  1. 1Circle the letter of the best answer. Show how you know.

    How does absolute value help you find the distance between (0, −4) and (0, 6)?

    1. ASubtract |−4| from |6| to get 2 units
    2. BAdd |−4| and |6| to get 10 units
    3. CMultiply |−4| by |6| to get 24 units
    4. DAbsolute value is not used for distance
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    Designing the Town Square: a rectangular park will have an area of 240,000 square feet. Two vertices are already marked on the planning grid, 3 units apart, and each grid unit represents 100 feet. The two known vertices of the park are 3 units apart, and each grid unit represents 100 feet. What is the park's width in feet?

    1. A3 feet
    2. B30 feet
    3. C103 feet
    4. D300 feet
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  3. 3Circle the letter of the best answer. Show how you know.

    Designing the Town Square: a rectangular park will have an area of 240,000 square feet. Two vertices are already marked on the planning grid, 3 units apart, and each grid unit represents 100 feet. The park's area must be 240,000 sq ft and its width is 300 ft. What is its length?

    1. A720 feet
    2. B800 feet
    3. C80,000 feet
    4. D240,300 feet
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  4. 4Circle the letter of the best answer. Show how you know.

    Designing the Town Square: a rectangular park will have an area of 240,000 square feet. Two vertices are already marked on the planning grid, 3 units apart, and each grid unit represents 100 feet. The park's length is 800 feet, and each grid unit represents 100 feet. How many units below the known vertices do the new corners sit?

    1. A0.8 units
    2. B8 units
    3. C80 units
    4. D800 units
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  5. 5Circle the letter of the best answer. Show how you know.

    A rectangle has vertices (-1, 4), (5, 4), (5, 1), (-1, 1). What is its perimeter?

    1. A6 units
    2. B9 units
    3. C18 units
    4. D18 square units
    Formula
    Put the numbers in
    Work it out
    Answer with its unit

Explain your thinkingTake a side you both put under 'Slanted.' Why does subtracting coordinates give the wrong length there, and what has to be true about two vertices for subtraction to work?

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help