← Back to the activity

Year 10 Maths — 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.Which of these points is the same distance from the origin as (3, 4)?

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

  2. 2.Find the distance between the points (1, 2) and (4, 6). Give the answer in units.

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

  4. 4.Find the midpoint of the segment joining (2, 3) and (8, 11). What is its y-coordinate?

  5. 5.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) 0
    • c) 3
    • d) 1

  6. 6.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

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

  8. 8.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
    • 13
    • 10
    • 15

Answer key — Year 10 Maths — Distance and section formulas

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