Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.9

Lesson 7.6Determine Distance 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 find the distance between two points on the coordinate plane using absolute value.

Why This Matters Captain Vega has two treasure locations on her map: a buried chest at (-3, 2) and a hidden cave at (4, 2). Both are at the same height (y = 2) on the map. She needs to figure out how far apart they are so she knows how much rope to bring. Another pair of treasures is at (1, -3) and (1, 5) — same column, different rows. How far apart is each pair?

RememberDetermine Distance on the Coordinate Plane

Distance on the Coordinate Plane. Formula: Distance = |x1 − x2| (horizontal) or |y1 − y2| (vertical) Distance is how far apart two points are, and it is never negative. When two points share a row or a column, you can find the distance using their coordinates.

  1. Same quadrant / Same sign: Subtract absolute values of differing coordinates.
  2. Different quadrants / Opposite signs: Add absolute values of differing coordinates.
  3. Distance is never negative; it is zero when both points coincide

Words: Distance (Distancia)Absolute value (Valor absoluto)Horizontal distance (Distancia horizontal)Vertical distance (Distancia vertical)Coordinate plane (Plano cartesiano)

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

    What is the distance between (-4, 1) and (3, 1)?

    1. A-7 units
    2. B1 unit
    3. C7 units
    4. D12 units

    Hint The y's match (both 1), so it's a horizontal gap between x = -4 and x = 3.

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

    In which quadrant is the point (-4, 5)?

    1. AQuadrant I
    2. BQuadrant III
    3. CQuadrant II
    4. DQuadrant IV
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    Which point is located on the x-axis?

    1. A(-4, -4)
    2. B(0, 4)
    3. C(4, 4)
    4. D(4, 0)
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    A point has a positive x-coordinate and a negative y-coordinate. Which quadrant is it in?

    1. AQuadrant I
    2. BQuadrant II
    3. CQuadrant IV
    4. DQuadrant III
    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    A drone starts at position (-4, 0) on a grid and needs to deliver a package to (3, 0), then fly to another delivery at (3, -5). It can only fly horizontally or vertically. What is the horizontal distance from (−4, 0) to (3, 0)?

    1. A1 unit
    2. B−1 unit
    3. C7 units
    4. D12 units
    Show your work
  6. 6Circle the letter of the best answer. Show how you know.

    A drone starts at position (-4, 0) on a grid and needs to deliver a package to (3, 0), then fly to another delivery at (3, -5). It can only fly horizontally or vertically. What is the vertical distance from (3, 0) to (3, −5)?

    1. A3 units
    2. B5 units
    3. C−5 units
    4. D8 units
    Show your work

Explain your thinkingHow did you use coordinates and absolute value to find the distance between two points in the same row or column?

Sentence starter The points ___ and ___ share the same ___ -coordinate. To find the distance, I found |___| + |___| = ___, which equals ___ units.

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.NOS.9

Lesson 7.6Determine Distance 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 find the distance between two points on the coordinate plane using absolute value.

Why This Matters Captain Vega has two treasure locations on her map: a buried chest at (-3, 2) and a hidden cave at (4, 2). Both are at the same height (y = 2) on the map. She needs to figure out how far apart they are so she knows how much rope to bring. Another pair of treasures is at (1, -3) and (1, 5) — same column, different rows. How far apart is each pair?

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Match each pair of city landmarks to the number of blocks between them.

    1. Subway (1, 6) to Tower (8, 6)
    2. Market (-3, -1) to Stadium (-3, 7)
    3. Bank (2, 3) to Library (2, 9)
    4. Café (-2, 1) to Gym (-2, -4)
    • A7 blocks
    • B8 blocks
    • C6 blocks
    • D5 blocks
  2. 2Write the name of the correct group on each line.

    Sort each block-distance problem by whether you SUBTRACT (same side of zero) or ADD absolute values (opposite sides of zero).

    Groups: Same side of zero — subtract Opposite sides of zero — add absolute values
    • School (2, 3) to Library (2, 9)
    • Subway (1, 6) to Tower (8, 6)
    • Park (-4, 5) to City Hall (3, 5)
    • Café (-2, 1) to Gym (-2, -4)
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    A drone starts at position (-4, 0) on a grid and needs to deliver a package to (3, 0), then fly to another delivery at (3, -5). It can only fly horizontally or vertically. What is the total flight path?

    1. A2 units
    2. B7 units
    3. C12 units
    4. D35 units
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    The Bank is at (2, 3) and the Library is at (2, 9). How many blocks apart are they?

    1. A3 blocks
    2. B6 blocks
    3. C11 blocks
    4. D12 blocks
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    The Park is at (-4, 5) and City Hall is at (3, 5). How many blocks apart are they?

    1. A1 block
    2. B5 blocks
    3. C7 blocks
    4. D12 blocks
    Show your work
  4. 6Circle the letter of the best answer. Show how you know.

    The Café is at (-2, 1) and the Gym is at (-2, -4). How many blocks apart are they?

    1. A2 blocks
    2. B3 blocks
    3. C5 blocks
    4. D6 blocks
    Show your work

Explain your thinkingHow did you use coordinates and absolute value to find the distance between two points in the same row or column?

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