Discussion
If \(O\) is the origin and \(C\) is the midpoint of \(A(-2, 1)\) and \(B(4, -3)\) , then \(\vec{OC}\) is
Answer: D
\(\vec{OC} = \hat{i} - \hat{j}\).
The midpoint of \(A(-2, 1)\) and \(B(4, -3)\) is
\[ \begin{aligned} C &= \left(\frac{-2 + 4}{2}, \frac{1 + (-3)}{2}\right) \\ &= (1, -1) \end{aligned} \]
so its position vector from the origin is \(\hat{i} - \hat{j}\). \(-\hat{i} + \hat{j}\) has both signs reversed, \(\hat{i} + \hat{j}\) gets the y-coordinate's sign wrong, and \(\frac{1}{2}\hat{i} + \frac{1}{2}\hat{j}\) halves the wrong sums.
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