Question

If R is (-4, 7) and S is (-2, 12), what is the component form of the vector R.S?
(8,84)
(2,5)
(-6, 19)
(-3,9.5)

Answer 1

Answer:

(2, 5)

Step-by-step explanation:

Given:

• R = (-4, 7)
• S = (-2, 12)

To find the components of $\overrightarrow{RS}$ we need to go from R to O and then O to S.  Remember that $\overrightarrow{RO}$ is the negative of $\overrightarrow{OR}$.  Therefore:

$\begin{aligned} \displaystyle \overrightarrow{RS} & =\overrightarrow{RO}+\overrightarrow{OS}\\& = \overrightarrow{OS}-\overrightarrow{OR}\\& =\binom{-2}{12}-\binom{-4}{7}\\& =\binom{2}{5}\end{aligned}$

Therefore, the component form (x, y) of the vector $\overrightarrow{RS}$ is (2, 5)