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Grade 10 Math — Distance and section formulas

Find the distance between two points, the point that divides a segment in a given ratio, and the area of a triangle from its vertices.

Name: ________________________

  1. 1.The point P divides the segment joining (1, 2) and (7, 11) in the ratio 2 : 1, measured from (1, 2). What is the y-coordinate of P?

  2. 2.Which of these points is the same distance from the origin as (3, 4)?

    • a) (1, 6)
    • b) (2, 3)
    • c) (4, 4)
    • d) (5, 0)

  3. 3.How far is the point (7, 24) from the origin? Give the answer in units.

  4. 4.This line runs from 0 to 10. Tap the point that divides it in the ratio 2 : 3, measured from 0.

    Mark the line with an X.

    012345678910

  5. 5.Find the area of the triangle whose vertices are (0, 0), (4, 0) and (0, 6). Give the answer in square units.

  6. 6.Match each pair of points to the distance between them, in units.

    • (0, 0) and (5, 12)
    • (0, 0) and (9, 12)
    • (0, 0) and (8, 6)
    • (1, 1) and (4, 5)
    • 5
    • 10
    • 15
    • 13

  7. 7.Find the area of the triangle whose vertices are (2, 1), (8, 1) and (2, 9). Give the answer in square units.

  8. 8.What is the area of the triangle whose vertices are (1, 2), (2, 4) and (3, 6)? Give the answer in square units.

    • a) 2
    • b) 1
    • c) 3
    • d) 0

Answer key — Grade 10 Math — Distance and section formulas

  1. 1. 8
  2. 2. d) (5, 0)
  3. 3. 25
  4. 4. 4
  5. 5. 12
  6. 6. (0, 0) and (5, 12) → 13; (0, 0) and (9, 12) → 15; (0, 0) and (8, 6) → 10; (1, 1) and (4, 5) → 5
  7. 7. 24
  8. 8. d) 0