Answer:
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!