Year 9 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.Find the distance between the points (1, 2) and (4, 6). Give the answer in units.
2.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?
3.Which of these points is the same distance from the origin as (3, 4)?
- a) (4, 4)
- b) (5, 0)
- c) (2, 3)
- d) (1, 6)
4.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?
5.Find the area of the triangle whose vertices are (2, 1), (8, 1) and (2, 9). Give the answer in square units.
6.Find the distance between the points (0, 0) and (6, 8). Give the answer in units.
7.Find the area of the triangle whose vertices are (0, 0), (4, 0) and (0, 6). Give the answer in square units.
8.Find the midpoint of the segment joining (2, 3) and (8, 11). What is its x-coordinate?

Answer key — Year 9 Maths — Distance and section formulas