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 = [tex]\frac{mx2+nx1}{m+n}[/tex]
- y = [tex]\frac{my2+ny1}{m+n}[/tex]
∵ 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 = [tex]\frac{1(4)+2(-5)}{1+2}[/tex] = [tex]\frac{4-10}{3}[/tex] = [tex]\frac{-6}{3}[/tex]
∴ x = -2
∵ y = [tex]\frac{1(-7)+2(5)}{1+2}[/tex] = [tex]\frac{-7+10}{3}[/tex] = [tex]\frac{3}{3}[/tex]
∴ y = 1
∴ The coordinates of point P are (-2, 1)
