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

Lesson 7.6Comparing Distances on the Plane

Apply Day · Set BSecond form · new problems, same idea

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
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Learning target I can find the distance between two points on the coordinate plane using absolute value.

Remember7.6 · Part II

Distance on the Coordinate Plane

  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. 1Complete each step, then write the final answer.

    Find the distance between (1, 5) and (7, 5).

    Show your work
    Final answer:
  2. 2Complete each step, then write the final answer.

    Find the distance between (−4, −3) and (−4, 6).

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    Point P is at (−2, 5). Point Q has the same x-coordinate and is 8 units from P. Q is in Quadrant III. What is the y-coordinate of Q?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    In a video game, a player stands at (4, −3). A coin is at (4, 5). How many units must the player move to reach the coin?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    A drone flies straight up from (−3, −6.5) to (−3, 2) on a radar grid. How many units does it fly?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.

    Deon walks east from (−2.5, 3) to (4, 3). Then he walks south to (4, −1.5). How many units does he walk in all?

    Show your work
    Final answer:
  7. 7Circle the letter of the best answer. Show how you know.

    What is the distance between (-4, 3) and (2, 3)?

    1. A2 units
    2. B4 units
    3. C6 units
    4. D8 units
    Show your work
  8. 8Circle the letter of the best answer. Show how you know.

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

    1. A2 units
    2. B4 units
    3. C6 units
    4. D10 units
    Show your work
  9. 9Circle the letter of the best answer. Show how you know.

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

    1. A8 units
    2. B12 units
    3. C14 units
    4. D20 units
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
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