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8th grade · Math · Unit 18 of 19

Distance on a Grid

Pythagoras between two points

What your child practices

Finding the straight-line distance between two points on a coordinate grid by drawing a right triangle and using the Pythagorean Theorem, a² + b² = c².

New York State Learning Standards learning standard: NY-8.G.8 · applying the Pythagorean Theorem to find the distance between two points in a coordinate system

How we explain it

Children can open this short lesson before they practice.

  1. Draw a right triangle between the two points: one leg across, one leg up or down.
  2. The legs are the differences of the x-coordinates and of the y-coordinates.
  3. Use a² + b² = c². The distance is c.

Example: What is the distance between (1, 2) and (4, 6)? Across: 4 − 1 = 3. Up: 6 − 2 = 4. 3² + 4² = 9 + 16 = 25. c = √25 = 5. Answer: 5 units

Distance on a Grid in New York

In the New York State Learning Standards, this is unit 18 of 19 in 8th grade Math, after Slope & Rate of Change and before Lines of Best Fit.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: New York State Education Department (NYSED)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    What is the distance between A(−2, 1) and B(−14, −4)?

    • 13
    • 17
    • 14
    • 12

  2. Question 2

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

    • √21
    • √7
    • 7
    • √29

  3. Question 3

    Which point is 5 units from the origin (0, 0)?

    • (2, 3)
    • (1, 4)
    • (5, 5)
    • (3, 4)

  4. Question 4

    To find the distance from (2, −2) to (6, −5), what are the legs of the right triangle?

    • 8 and 7
    • 4 and 3
    • 5 and 4

  5. Question 5

    On a map grid where each unit is 1 mile, a library is at (4, 3) and a museum is at (10, 11). How far apart are they in a straight line, in miles?

    • 14
    • 8
    • 11
    • 10

  6. Question 6

    What is the distance between A(1, −3) and B(5, 0)?

    • 5
    • 6
    • 7
    • 4

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