Final answer:
To find point Q on the line segment from R (-3, 3) to S (6, -3) that divides it in a 2:1 ratio, we use the section formula. The coordinates of point Q are calculated to be (3, -1), aligning with option a.
Step-by-step explanation:
Finding Point Q on a Directed Line Segment
The question is asking to find point Q that divides the line segment from point R (-3, 3) to point S (6, -3) in the ratio 2:1. This can be done using the section formula which is a part of coordinate geometry in mathematics. To find the coordinates of point Q, we apply the following formula:
Q(x, y) = ((m*x2 + n*x1) / (m + n), (m*y2 + n*y1) / (m + n))
Where R(x1, y1) = (-3, 3), S(x2, y2) = (6, -3), and the ratio m:n = 2:1.
Substituting the values, we get Q's coordinates:
Q(x) = ((2 * 6 + 1 * (-3)) / (2 + 1)) = (12 - 3) / 3 = 9 / 3 = 3
Q(y) = ((2 * (-3) + 1 * 3) / (2 + 1)) = (-6 + 3) / 3 = -3 / 3 = -1
Thus, point Q is (3, -1), which corresponds to option a.