Question

Find the point Q along the directed line segement from point R (-3, 3) to point S(6, -3) that divides the segment in the ratio 2:1.

A. (3, 0)
B. (3, -1)
C. (6, -4)
D. (0, 1)

Answer 1

Hello,

Explanation:

`\overrightarrow{RS}=\left(\begin{array}{c}6\\ -3\end{array}\right)-\left(\begin{array}{c}-3\\ 3\end{array}\right)=\left(\begin{array}{c}9\\ -6\end{array}\right)\\\\\overrightarrow{RQ}=(2)/(3)\overrightarrow{RS} =(2)/(3)*\left(\begin{array}{c}9\\ -6\end{array}\right)=\left(\begin{array}{c}6\\ -4\end{array}\right)\\\\`

`\overrightarrow{OQ}=\overrightarrow{OR}+\overrightarrow{RQ}\\=\left(\begin{array}{c}-3\\ 3\end{array}\right)+\left(\begin{array}{c}6\\ -4\end{array}\right)=\left(\begin{array}{c}3\\ -1\end{array}\right)\\Answer\ is\ \boxed{B}`