Question

Suppose, in triangle $\triangle ABC$, $x - y + 5 = 0$, $x + 2y = 0$ are respectively the equations of the perpendicular bisectors of the sides $AB$ and $AC$. If $A$ is $(1, -2)$, the equation of the line joining $B$ and $C$ is

• A. $6x + 7y = 0$
• B. $14x + 23y - 40 = 0$
• C. $2x - 11y = 0$
• D. $2x + y = 0$

Hint:

Use perpendicular bisector properties to locate points and apply two-point form for line equation.

Answer 1

The Correct Option is B

Let $M$ and $N$ be midpoints of $AB$ and $AC$ respectively. Given that the perpendicular bisectors pass through $M$ and $N$, and $A = (1, -2)$ lies on both $AB$ and $AC$
Using geometry and solving the system of equations:
From $x - y + 5 = 0$ and $x + 2y = 0$, determine points $B$ and $C$ using reflection or coordinate geometry
Finally determine coordinates of $B$ and $C$, then find line $BC$ equation through two-point form
The line joining them is $14x + 23y - 40 = 0$