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

Answer:

K(8, 4)

Step-by-step 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:

$x = \frac{mx_2 + nx_1}{m + n}$

$y = \frac{my_2 + ny_1}{m + n}$

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:

$x = \frac{mx_2 + nx_1}{m + n}$

$x = \frac{3(12) + 2(2)}{3 + 2}$

$x = \frac{36 + 4}{5}$

$x = \frac{40}{5}$

$x = 8$

$y = \frac{my_2 + ny_1}{m + n}$

$y = \frac{3(6) + 2(1)}{3 + 2}$

$y = \frac{18 + 2}{5}$

$y = \frac{20}{5}$

$y = 4$

The coordinates of K = (8, 4)