Question

The equation of line bisecting perpendicularly the segment joining the points $(-4,6)$ and $(8,8)$ is

• A. $y=7$
• B. $6x+y-19=0$
• C. $x+2y-7=0$
• D. $6x+2y-19=0$

Answer 1

Answer: (B)

$6x+y-19=0$

Since the line is perpendicular to the one joining the given points, whose slope is $\frac{8-6}{8+4}=\frac{2}{12}=\frac{1}{6}$

for the slope of the perpendicular line: $m_{perp}\times \frac{1}{6}=-1\Rightarrow m_{perp}=-6$

the slope of the perpendicular line becomes $-6$

Also the line passes through the midpoint of the two given points, which is $(\frac{-4+8}{2},\frac{6+8}{2})=(2,7)=(x_1,y_1)$

The equation of the line thus becomes $y=-6x+c$........(i)

Putting value of $(x_1,y_1)$ in (i)

now, $y_1=-6x_1+c\Rightarrow 7=-6\times 2+c\Rightarrow c=7+12=19$

i.e. $y+6x-19=0$