If the perpendicular bisector of the line joining $P(1,4)$ and $Q(k,3)$ has y-intercept $-4$, then the possible values of $k$ are
- A. -2 and 2
- B. -1 and 1
- C. -3 and 3
- D. -4 and 4
✅ Correct Answer: -4 and 4
Explanation
Slope of $PQ$ $= (3-4)/(k-1) = -1/(k-1)$ Slope of perpendicular bisector $= k-1$ Midpoint of $PQ$ $= ((k+1)/2, 7/2)$ Equation gives y-intercept $-4$ Solving gives $k^2 = 16$ $k = \pm 4$
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