Vector Algebra
Position Vectors and Midpoint
Grade 12
Question:
<p>If O is origin and C is the mid-point of A(2, -1) and B(-4, 3), then the value of OC is</p>
<p>(a) <strong>i</strong> + <strong>j</strong></p>
<p>(b) <strong>i</strong> - <strong>j</strong></p>
<p>(c) -<strong>i</strong> + <strong>j</strong></p>
<p>(d) -<strong>i</strong> - <strong>j</strong></p>
Step-by-Step Solution
Key Concept: Use the midpoint formula; express coordinates as position vectors.
Solution: The mid-point C of A(2, -1) and B(-4, 3) is given by: C = \(\left(\frac{2 + (-4)}{2}, \frac{-1 + 3}{2}\right) = \left(\frac{-2}{2}, \frac{2}{2}\right) = (-1, 1)\) Therefore, the position vector OC = - i + j
Correct Answer: C