Answer:
(-3, 2)
Step-by-step explanation:
Given that point Q, partitions segment PE, such that PQ:QE is 1:3, coordinates of point Q is found using the formula below:
[tex] x = \frac{mx_2 + nx_1}{m + n} [/tex]
[tex] y = \frac{my_2 + ny_1}{m + n} [/tex]
Where,
[tex] P(-4, 4) = (x_1, y_1) [/tex]
[tex] E(0, -4) = (x_2, y_2) [/tex]
[tex] m = 1, n = 3 [/tex]
Plug in the necessary values to find x and y coordinates for point Q as follows:
[tex] x = \frac{mx_2 + nx_1}{m + n} [/tex]
[tex] x = \frac{1(0) + 3(-4)}{1 + 3} [/tex]
[tex] x = \frac{0 - 12}{4} [/tex]
[tex] x = \frac{-12}{4} [/tex]
[tex] x = -3 [/tex]
[tex] y = \frac{my_2 + ny_1}{m + n} [/tex]
[tex] y = \frac{1(-4) + 3(4)}{1 + 3} [/tex]
[tex] y = \frac{-4 + 12}{4} [/tex]
[tex] y = \frac{8}{4} [/tex]
[tex] y = 2 [/tex]
The coordinates of the point Q are (-3, 2))
