Question

Name

Answer 1

Answer:

The coordinates of point P are (-2, 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 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 = $\frac{1(4)+2(-5)}{1+2}$ = $\frac{4-10}{3}$ = $\frac{-6}{3}$

∴ x = -2

∵ y = $\frac{1(-7)+2(5)}{1+2}$ = $\frac{-7+10}{3}$ = $\frac{3}{3}$

∴ y = 1

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