Straight Lines
Perpendicular Bisector
AIEEE 2008
Grade 11
Question:
The perpendicular bisector of the segment joining $P(1, 4)$ and $Q(k, 3)$ has $y$-intercept $-4$. Find the positive value of $k$.
Step-by-Step Solution
Key Concept: The perpendicular bisector passes through the midpoint of $PQ$ with slope $= -(1/\text{slope of } PQ)$. Write its equation, set $x = 0$ to get the $y$-intercept, and solve for $k$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: 4