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.

Answer 1

Answer:

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

Step-by-step 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 = $\frac{mx2+nx1}{m+n}$

• y = $\frac{my2+ny1}{m+n}$

∵ 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 = $\frac{2(-10)+3(5)}{2+3}$ = $\frac{-20+15}{5}$ = $\frac{-5}{5}$

∴ x = -1

∵ y = $\frac{2(11)+3(-9)}{2+3}$ = $\frac{22-27}{5}$ = $\frac{-5}{5}$

∴ y = -1

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