First slide

Equation of line in Straight lines

Question

If the perpendicular bisector of the line segment joining $P (1, 4)$ and $Q (k, 3)$ has y-intercept $- 4 .$ Then, a possible value of $k,$ is

Moderate

A

$- 2$
B

$- 4$
C

$1$
D

$2$

Solution

The coordinates of the mid-point of $P Q$ are $(\frac{k + 1}{2}, \frac{7}{2}) .$
Slope of $P Q = \frac{4 - 3}{1 - k} = \frac{1}{1 - k}$
$∴$ Slope of the perpendicular bisector of $P Q$ is $(k - 1) .$
The equation of the perpendicular bisector of $P Q,$ is
$y - \frac{7}{2} = (k - 1) (x - \frac{k + 1}{2})$
It passes through $(0, - 4)$
$∴ - \frac{15}{2} = - \frac{(k^{2} - 1)}{2} \Rightarrow k = \pm 4$

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