Question

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

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

Answer 1

Answer: (A)

$6 x + y - 19 = 0$

Answer 2

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

$y - 6 = \frac { 8 - 6 } { 8 + 4 } ( x + 4 )$ ⇒ $y - 6 = \frac { 2 } { 12 } ( x + 4 )$

⇒ $6 y - x = 40$ ......(i)

Now equation of any line $\perp$ 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)

$\therefore$ From (ii) 12 + 7 + $\lambda = 0$ ⇒ $\lambda = - 19$ ,

$\therefore$ Equation of line is $6 x + y - 19 = 0$