Question

Name

PARTITION A DIRECTED LINE SEGMENT
1. Given G(-5,5) and H(4, -7), find the coordinates of p so that p partitions GH in the ratio 1:2.
Point P?

Answer 1

The coordinates of point P are (-2, 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 GH in a ratio 1: 2

∴ P = (x, y)

∴ m = 1 and n = 2

∵ G = (-5, 5) and H = (4, -7)

∴ x1 = -5 and x2 = 4

∴ y1 = 5 and y2 = -7

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

∵ x =
`(1(4)+2(-5))/(1+2)` =
`(4-10)/(3)` =
`(-6)/(3)`

∴ x = -2

∵ y =
`(1(-7)+2(5))/(1+2)` =
`(-7+10)/(3)` =
`(3)/(3)`

∴ y = 1

∴ The coordinates of point P are (-2, 1)