Question

What are the coordinates of the point on the directed line segment from (-6, -10)to (6,8) that partitions the segment into a ratio of 2 to 1?

Answer 1

The coordinates of the point that divides the coordinates given into ratio 2 to 1 = (2, 2)

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) is (-6, -10) and (6,8)

x₂ = 6

x₁ = -6

y₂ = 8

y₁ = -10

m = 2

n = 1

x = [(mx₂ + nx₁)/(m + n)]

x = [(2×6 + 1×-6)/(2 + 1)]

x = (6/3) = 2

y = [(my₂ + ny₁)/(m + n)]

y = [(2×8 + 1×-10)/(2 + 1)]

y = (6/3) = 2

Hence, the coordinates of the point that divides the coordinates given into ratio 2 to 1 = (2, 2)

Hope this Helps!!!