Question

3.

On a coordinate plane, a line segment has P(6,2) and Q(3,8).

Point M lies on PQ and divides the segment so that the ratio

of PM:MQ is 3:2. What are the coordinates of point M?

A. (4.5, 5.0)

B. (5.6, 4.2)

C. (4.8, 4.4)

D. (4.2, 5.6)

Answer 1

`M(x,y) = (4.8,4.4)`

Explanation:

Given

`P(x_1,y_1) = (6,2)`

`Q(x_2,y_2) = (3,8)`

`m:n = PM:MQ = 3 : 2`

Required

Determine the coordinates of M

To solve this, we make use of the following partition formula:

`M(x,y) = ((nx_2+mx_1)/(n+m),(ny_2+my_1)/(n+m))`

Substitute values for m, n, x's and y's

`M(x,y) = ((2*3+3*6)/(2+3),(2*8+3*2)/(2+3))`

`M(x,y) = ((24)/(5),(22)/(5))`

`M(x,y) = (4.8,4.4)`

Option D is correct