Question

2. Given HS has endpoints H(5, -9) and S(-10, 11), find the coordinates of P so that P partitions HS in a ratio 2:3.

Point P?

Answer 1

The coordinates of point P are (-1, -1)

Explanation:

The coordinates of the partition point (x, y) of a line segment whose endpoints are (x1, y1) and (x2, y2) at ratio m: n are

• x =
  `(mx2+nx1)/(m+n)`

• y =
  `(my2+ny1)/(m+n)`

∵ P partitions segment HS in a ratio 2: 3

∴ P = (x, y)

∴ m = 2 and n = 3

∵ H = (5, -9) and S = (-10, 11)

∴ x1 = 5 and x2 = -10

∴ y1 = -9 and y2 = 11

→ Substitute them in the rule above to find x and y

∵ x =
`(2(-10)+3(5))/(2+3)` =
`(-20+15)/(5)` =
`(-5)/(5)`

∴ x = -1

∵ y =
`(2(11)+3(-9))/(2+3)` =
`(22-27)/(5)` =
`(-5)/(5)`

∴ y = -1

∴ The coordinates of point P are (-1, -1).