Question

If in a parallelogram $ABDC$, the coordinates of $A,B$ and $C$ are respectively $(1,2),(3,4)$ and $(2,5)$, then the equation of the diagonal $AD$ is :

• A. $5x+3y-11=0$
• B. $5x-3y+1=0$
• C. $3x-5y+7=0$
• D. $3x+5y-13=0$

Answer 1

The correct option is B $5x-3y+1=0$


Diagonals of a parallelogram bisect each other.
$\therefore (\frac{x_1+1}{2},\frac{y_1+2}{2})=(\frac{3+2}{2},\frac{5+4}{2})$
$\Rightarrow \frac{x_1+1}{2}=\frac{5}{2}\Rightarrow x_1=4$
and $\frac{y_1+2}{2}=\frac{9}{2}\Rightarrow y_1=7$

$\therefore$ Coordinates of $D$ is $(4,7)$
$\therefore$ Equation of $AD$ is
$\frac{y-2}{x-1}=\frac{7-2}{4-1}$

$\Rightarrow \frac{y-2}{x-1}=\frac{5}{3}$

$\Rightarrow 3y-6=5x-5$
$\Rightarrow 5x-3y+1=0$