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10th grade The distance formula worksheet

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The distance formula

Grade 10 Math Worksheet

NameDate

Circle the best answer.

  1. Pia plots quadrilateral ABCD with A(0, 0), B(4, 3), C(9, 3) and D(5, 0). What is ABCD, and what is its perimeter?

    • A rhombus with perimeter 20
    • A rectangle with perimeter 20
    • A rhombus with perimeter 28
    • A square with perimeter 20

  2. Milo's tent has corners A(0, 0), B(8, 0) and C(1, 6). M is the midpoint of AB. How long is the median CM?

    • 3√5
    • √37
    • √85
    • 45

  3. A(2, y) and B(8, 2) with AB = 10. Esme's points are A(2, y) and B(8, 2), and AB = 10. Which values of y work?

    • y = 10 or y = -6
    • y = 8 or y = -8
    • y = 10 alone
    • y = 12 or y = -8

  4. Kira's dart board is the circle (x − 2)² + (y + 3)² = 25. A dart lands at P(6, -1). Is P inside, on, or outside the circle?

    • Outside: 20 is greater than the radius 5
    • Inside: 4² + 2² = 20, which is less than 25
    • Outside: (6 − 2)² + (-1 − 3)² = 32 is more than 25
    • Outside: 4 + 2 = 6 is more than the radius 5

  5. A(1, 3), B(5, -1) and a point P(x, 0) on the x-axis with PA = PB. Tala wants a point P(x, 0) on the x-axis equally far from A(1, 3) and B(5, -1). What is x?

    • -2
    • 2
    • 4
    • 6

  6. Noah checks A(0, 0), B(3, 4) and C(9, 12). AB = 5, BC = 10 and AC = 15. What do the distances show?

    • They are collinear if and when AB = BC
    • The points are collinear, since AB + BC = AC
    • They form a triangle, since the three distances are different
    • They form a right triangle, since 5 + 10 = 15

  7. Zee compares two drones measured from the origin: P at (5, -5) and Q at (-7, 2). Which is closer to the origin?

    • P: its distance √50 is less than √53
    • Q: its legs add to 7 + 2 = 9, less than 5 + 5 = 10
    • They are equally far, since 5 and 7 are close
    • Q: -7 + 2 = -5 is smaller than 5 + (-5) = 0

  8. Ari's hiking route runs from A(-4, 2) to B(6, -4), and M is its midpoint. How long is AM?

    • √68
    • 34
    • √34
    • 2√34

  9. Ren's tile △ABC has A(0, 0), B(6, 0) and C(0, 8). M is the midpoint of the hypotenuse BC. Which statement about M is true?

    • M is 7 from A and 5 from B and C
    • M is 5 from each of A, B and C
    • M is 25 from each of A, B and C
    • M is 5 from A but 10 from B and C

  10. Esme's garden has corners A(0, 0), B(5, 0), C(8, 4) and D(0, 4). How long is the fence around it?

    • 20 m
    • 22 m
    • 17 m
    • 24 m
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10th grade The distance formula worksheet – printable
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About this worksheet

The distance formula. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can find the legs of the right triangle under a segment by subtracting coordinates.
  • I can find a distance as a whole number, a simplified radical, or to the nearest tenth.
  • I can find a perimeter from coordinates and a missing coordinate from a distance.

Standard: G-GPE.B.7, G-GPE.B.4

Words to know

run, rise: The across leg (x₂ − x₁) and the up leg (y₂ − y₁).

distance formula: d = √(run² + rise²): the Pythagorean theorem written with coordinates.

simplified radical: A root with no square factor left inside: 2√13, not √52.

perimeter: The distance all the way around a shape.

Common mistakes

Added the run and the rise instead of using the Pythagorean theorem. That gives a walking distance along the grid, not the straight line.

Stopped at run² + rise², which is the length squared.

Did not square the legs, or halved the squared length. Each leg is squared before adding.

What to say

Ask: does the answer look too big for the segment?

Questions parents ask

What is the most common mistake with the distance formula?

Added the run and the rise instead of using the Pythagorean theorem. That gives a walking distance along the grid, not the straight line.

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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