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

Question

Aicharya · Accepted Answer

Since, in parallelogram mid points of both diagonals coinsides. $\therefore$ mid-point of $A D=$ mid-point of $B C$

$\left(\frac{x_{1}+1}{2}, \frac{y_{1}+2}{2}\right)=\left(\frac{3+2}{2}, \frac{4+5}{2}\right)$ $\therefore \quad\left(x_{1}, y_{1}\right)=(4,7)$ Then, equation of $A D$ is, $y-7=\frac{2-7}{1-4}(x-4)$ $y-7=\frac{5}{3}(x-4)$ $3 y-21=5 x-20$ $5 x-3 y+1=0$

If in a parallelogram $\mathrm{ABDC}$, the coordinates of $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are…

Solution