Question

What are the coordinates of the point on the directed line segment from (-8, 2) to (7, -3) that partitions the segment into a ratio of 3 to 2?

Answer 1

The coordinates of the point that partitions this into a ratio os 3 to 2 is

(1, -1)

Step-by-step explanation

Mathematically, if a point P(x, y) divides the coordinates (x₁, y₁) and (x₂, y₂) internally in the ratio m:n then point P(x, y) is given as

x = [(mx₂ + nx₁)/(m + n)]

y = [(my₂ + ny₁)/(m + n)]

For this question,

(x₁, y₁) and (x₂, y₂) are (-8, 2) and (7, -3)

m : n = 3 : 2

x₂ = 7

x₁ = -8

y₂ = -3

y₁ = 2

m = 3

n = 2

x = [(mx₂ + nx₁)/(m + n)]

x = [(3×7 + 2×-8)/(3 + 2)]

x = [(21 - 16)/(3 + 2)]

x = (5/5) = 1

y = [(my₂ + ny₁)/(m + n)]

y = [(3×-3 + 2×2)/(3 + 2)]

y = [(-9 + 4)/(3 + 2)]

y = (-5/5) = -1

Hope this Helps!!!