Question

If $A(-1,2),B(5,1),C(6,5)$ are the vertices of a parallelogram $ABCD$. The equation to the diagonal through $B$ is

• A. $x+y+6=0$
• B. $x+y-6=0$
• C. $x-y-4=0$
• D. $x-2y-1=0$

Answer 1

Answer: (B)

Diagonals of parallelogram bisects each other.
$\Rightarrow$ Diagonal $BD$ passes through mid point of $AC$.
i.e. $\left(\frac{5}{2},\frac{7}{2}\right)$
$\therefore$ Equation of diagonal passing through $(5,1)$ and $\left(\frac{5}{2},\frac{7}{2}\right)$ is
$y-1=\frac{\frac{7}{2}-1}{\frac{\frac{5}{2}}{2}-5}(x-5)$
$\Rightarrow y-1=-1(x-5)$
$\Rightarrow y+x-6=0$