Question

Prove that the diagonals of a rectangle ABCD with vertices A(2, −1), B(5, −1), C(5, 6) and D(2, 6) are
equal and bisect each other. [CBSE 2014]

Answer 1

The vertices of the rectangle ABCD are A(2, −1), B(5, −1), C(5, 6) and D(2, 6). Now
$$\begin{gathered} \mathrm{Coordinates}\mathrm{of}\mathrm{midpoint}\mathrm{of}AC=\left(\frac{2+5}{2},\frac{-1+6}{2}\right)=\left(\frac{7}{2},\frac{5}{2}\right) \\ \mathrm{Coordinates}\mathrm{of}\mathrm{midpoint}\mathrm{of}BD=\left(\frac{5+2}{2},\frac{-1+6}{2}\right)=\left(\frac{7}{2},\frac{5}{2}\right) \end{gathered}$$
Since, the midpoints of AC and BD coincide, therefore the diagonals of rectangle ABCD bisect each other.