If the midpoint of the line joining (1 – k, -4) and (2, k + 1) is (-k, k), find the value of k.
-
A.
-4 -
B.
-3 -
C.
-2 -
D.
-1
Correct Answer: Option 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)