If the perpendicular bisector of the line segment joining the points P(1,4) and Q(k,3) has…

Question

If the perpendicular bisector of the line segment joining the points $P(1,4)$ and $Q(k,3)$ has $y$-intercept equal to $-4$, then a value of $k$ is:

Accepted Answer

$${m_{PQ}} = {{4 - 3} \over {1 - k}} $$

$$ \therefore $$ Slope of perpendicular bisector of PQ, $$ {m_ \bot } = k - 1$$

mid point of PQ = $$\left( {{{k + 1} \over 2},{7 \over 2}} \right)$$

equation of perpendicular bisector

$$y - {7 \over 2} = (k - 1)\left( {x - {{k + 1} \over 2}} \right)$$

for y intercept put x = 0

$$y = {7 \over 2} - \left( {{{{k^2} - 1} \over 2}} \right) =  - 4$$

$${{{k^2} - 1} \over 2} = {{15} \over 2} \Rightarrow k =  \pm 4$$

Solutions · 1