Question

Find the coordinates of point Q that lies along the directed line segment from R(-2, 4) to S(18, -6) and partitions the segment in the ratio of 3:7.A. (4, 1)B. (16, -2)C. (6, -3)D. (8, -1)

Answer 1

The coordinates of the point which partitions a directed line segment AB at the ratio a:b from A(x1, y1) to B(x2, y2) is computed as follows:

`(x,y)=(x_1+(a)/(a+b)(x_2-x_1),y_1+(a)/(a+b)(y_2-y_1_{}))`

In this case, the segment goes from R(-2, 4) to S(18, -6), and the partition ratio is 3:7. Substituting into the above formula, we get:

`\begin{gathered} (x,y)=(-2+(3)/(3+7)(18-(-2)),4+(3)/(3+7)(-6-4)) \\ (x,y)=(-2+(3)/(10)\cdot20,4+(3)/(10)(-10)) \\ (x,y)=(4,1) \end{gathered}`