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The equation of the line bisecting perpendicularly the segment joining the points $(-4,6)$ and $(8,8)$ is
Option: 1
$6 x+y-19=0$

Option: 2
$y=7$

Option: 3
$6 x+2 y-19=0$

Option: 4
$x+2 y-7=0$

Answers (1)

best_answer

Equation of the line passing through $(-4,6)$ and $(8,8)$ is

$y-6=\frac{8-6}{8+4}(x+4) \Rightarrow y-6=\frac{2}{12}(x+4) \Rightarrow 6 y-x=40$ $........(i)$

Now equation of any line $\perp \text { to it is } 6 x+y+\lambda=0$ $........(ii)$

This line passes through the midpoint of $(-4,6)$ and $(8,8)$ i.e., $(2,7)$

$\therefore$ $\text { From (ii) } 12+7+\lambda=0 \Rightarrow \lambda=-19 \text {, }$ $\therefore \quad \text { Equation of line is }$

$6 x+y-19=0$

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