On a coordinate Plane, a line segment has endpoints P(6,2) and Q(3,8). Point M lies on Line segment PQ and divides the segment so that the ratio of PM:MQ is 3:2. What are the coordinates of Point M?

Question

On a coordinate Plane, a line segment has endpoints P(6,2) and Q(3,8). Point M lies on Line segment PQ and divides the segment so that the ratio of PM:MQ is 3:2. What are the coordinates of Point M?

Answer 1

Let M(x,y). Then vector PM = <x - 6, y - 2>, vector MQ = < 3 - x, 8 - y>;

from here (x - 6)/3 - x) = 3/2; from here 2(x - 6) = 3(3 - x), 2x - 12 = 9 - 3x, 5x = 21, x = 21/5 = 4.2;

(y - 2)/(8 - y) = 3/2, 2(y - 2) = 3(8 - y), 2y - 4 = 24 - 3y, 5y = 28, y = 28/5 = 5.6.

Answer M(4.2, 5.6)