Question

Segment PE has endpoints P(-4,4) and E(0,-4). Find the coordinates of point Q such that PQ:QE is 1:3. Enter the coordinates below

Answer 1

(-3, 2)

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:

`x = (mx_2 + nx_1)/(m + n)`

`y = (my_2 + ny_1)/(m + n)`

Where,

`P(-4, 4) = (x_1, y_1)`

`E(0, -4) = (x_2, y_2)`

`m = 1, n = 3`

Plug in the necessary values to find x and y coordinates for point Q as follows:

`x = (mx_2 + nx_1)/(m + n)`

`x = (1(0) + 3(-4))/(1 + 3)`

`x = (0 - 12)/(4)`

`x = (-12)/(4)`

`x = -3`

`y = (my_2 + ny_1)/(m + n)`

`y = (1(-4) + 3(4))/(1 + 3)`

`y = (-4 + 12)/(4)`

`y = (8)/(4)`

`y = 2`

The coordinates of the point Q are (-3, 2))