Question

The perpendicular bisector of the line segment joining the points A(–1, 3) and B(2, 4) cuts the y-axis at :

• A. (0, 5)
• B. (0, -5)
• C. (0, 4)
• D. (0, -4)

Answer 1

The Correct Option is A

The midpoint of $A(-1, 3)$ and $B(2, 4)$ is:
\[\text{Midpoint} = \left( \frac{-1 + 2}{2}, \frac{3 + 4}{2} \right) = \left( \frac{1}{2}, \frac{7}{2} \right)\]
The slope of $AB$ is:
\[\text{Slope} = \frac{4 - 3}{2 - (-1)} = \frac{1}{3}\]
The perpendicular slope is $-3$. Using the point-slope formula:
\[y - \frac{7}{2} = -3 \left( x - \frac{1}{2} \right)\]
Simplify to find the $y$-intercept ($x = 0$):
\[y = 5\]