Question

Find the location of point Q on directed line segment PS, such that PQ: QS is divided into a ratio of 3.2.

P(7,-6) S(-3,-1)

Answer 1

Point Q = (-6, 2/7)

Explanation:

To find the location of point Q on the directed line segment PS that divides PQ:QS in the ratio of 3:2, we can use the following formula:

Q = (2S + rP)/(2 + r)

where r is the ratio of PQ to QS, and Q is the point we are trying to find.

Substituting the given values, we get:

r = PQ/QS = 3/2

Q = (2(-3,-1) + (3/2)(7,-6))/(2 + 3/2)

Q = (-6,-2 + (9/2))/7/2

Q = (-6,-2 + 9/7)

Therefore, the location of point Q on the directed line segment PS that divides PQ:QS in the ratio of 3:2 is approximately (-6, 0.29) or (-6, 2/7).

Hope this helps!