contestada

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)

Respuesta :

MrRoyal

Answer:

[tex]M(x,y) = (4.8,4.4)[/tex]

Step-by-step explanation:

Given

[tex]P(x_1,y_1) = (6,2)[/tex]

[tex]Q(x_2,y_2) = (3,8)[/tex]

[tex]m:n = PM:MQ = 3 : 2[/tex]

Required

Determine the coordinates of M

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

[tex]M(x,y) = (\frac{nx_2+mx_1}{n+m},\frac{ny_2+my_1}{n+m})[/tex]

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

[tex]M(x,y) = (\frac{2*3+3*6}{2+3},\frac{2*8+3*2}{2+3})[/tex]

[tex]M(x,y) = (\frac{24}{5},\frac{22}{5})[/tex]

[tex]M(x,y) = (4.8,4.4)[/tex]

Option D is correct