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Year 11 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.Find the distance between the points (0, 0) and (6, 8). Give the answer in units.

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

  3. 3.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)
    • 15
    • 13
    • 10
    • 5

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

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

  6. 6.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?

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

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

  8. 8.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

Answer key — Year 11 Maths — Distance and section formulas

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