Question

The endpoints of (MP)are M(2,1) and P(12,6). If point K partitions (MP) in a ratio of MK:KP = 3:2, what are the coordinates of K?

Answer 1

K(8, 4)

Explanation:

Given:

M(2, 1), P(12, 6)

MK:KP = 3:2

Required:

Coordinates of K

SOLUTION:

Coordinates of K can be determined using the formula below:

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

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

Where,

`M(2, 1) = (x_1, y_1)`

`P(12, 6) = (x_2, y_2)`

`m = 3, n = 2`

Plug in the necessary values to find the coordinates of K:

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

`x = (3(12) + 2(2))/(3 + 2)`

`x = (36 + 4)/(5)`

`x = (40)/(5)`

`x = 8`

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

`y = (3(6) + 2(1))/(3 + 2)`

`y = (18 + 2)/(5)`

`y = (20)/(5)`

`y = 4`

The coordinates of K = (8, 4)