If the midpoint of the line joining (1 – k, -4) and (2, k + 1) is (-k, k), find the value of k.
- -4
- -3
- -2
-
-1
The correct answer is: D
Explanation
Midpoint between \((x_{1}, y_{1})\) and \((x_{2}, y_{2})\) = \((\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})\).
\((-k, k) = (\frac{2 + (1 + k)}{2}, \frac{-4 + (k + 1)}{2})\)
\(-k = \frac{k + 3}{2} \implies -2k = k + 3\)
\(-3k = 3 \implies k = -1\)