Question

$ABCD$ is a square. Points $E(4,3)$ and $F(2,5)$ lie on $AB$ and $CD$, respectively, such that $EF$ divides the square in two equal parts. If the coordinates of $A$ are $(7,3)$, the other coordinates of the vertices can be

Answer 1

$\begin{array}{c}EismidpointofAB\\ \therefore coordinateofB\left(x,y\right)\\ \Rightarrow \frac{x+7}{2}=4\\ \Rightarrow x=1,\frac{3+y}{2}=3,y+3=6,y=3\end{array}$

and mid point of EF are point of interaction of diagonals.

$\begin{array}{c}\left(\frac{4+2}{2}\right)=3,\left(\frac{3+5}{2}\right)=4\\ \therefore 0\left(3,4\right)\end{array}$

Hence coordinate of D,

$\begin{array}{c}\Rightarrow \frac{x_1+1}{2}=3,x_1+1=-6,x_1=5\\ \frac{y_1+3}{2}=4,y_1+3=8,y=5\end{array}$

and coordinate of C, $\left(x_2,y_2\right)$

$\begin{array}{c}\Rightarrow \frac{x_2+7}{2}=3,x_2=1\\ \Rightarrow \frac{y_2+3}{2}=4,y_2=5\end{array}$