Question

4.Directed line segment PT has endpoints whose coordinates are P(-2,1) and T(4,7). Determine the coordinates ofpoint J that divides the segment into the ratio 2:1. [4 pts)

Answer 1

The coordinates of point J = (2, 5)

Step-by-step explanation

Mathematically, if a point J(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 (-2, 1) and (4, 7)

m:n = 2:1

x₂ = 4

x₁ = -2

y₂ = 7

y₁ = 1

m = 2

n = 1

Point J is then described with coordinates

x = [(mx₂ + nx₁)/(m + n)]

x = [(2×4 + 1×-2)/(2+1)] = (8 - 2)/3 = (6/3) = 2

y = [(my₂ + ny₁)/(m + n)]

y = [(2×7 + 1×1)/(2+1)] = (14 + 1)/3 = (15/3) = 5

Hence, the coordinates of point J is given as

(x, y) = (2, 5)

Hope this Helps!!!