The coordinates of F is (8.5, 7)
How to determine the coordinates of F?
The coordinates of the points are given as:
D = (-2, -5)
F = (5, 3)
DF : FE = 4 : 2
Rewrite the ratio as
m = 4 : 2
The coordinate of the partition is calculated as:
F = 1/(m + n) * (mx2 + nx1, my2 + ny1)
This gives
(5, 3) = 1/(4 + 2) * (4 * x + 2 * -2, 4 * y + 2 * -5)
Evaluate the sum and the product
(5, 3) = 1/6 * (4x - 4, 4y - 10)
Multiply both sides by 6
(30, 18) = (4x - 4, 4y - 10)
By comparison, we have:
4x - 4 = 30
4y - 10 = 18
Solve the equations
x = 8.5
y = 7
So, we have:
F = (8.5, 7)
Hence, the coordinates of F is (8.5, 7)
Read more about line partition at:
https://brainly.com/question/12959377
#SPJ1
