Question

A square is formed by the points $(4,5),(12,5),(12,-3)$ and $(4,-3)$. Find the coordinates of the point at which the diagonals of the square intersect.

• A. $(8,5)$
• B. $(9,6)$
• C. $(8,1)$
• D. $(12,1)$

Answer 1

The correct option is C $(8,1)$

We know that the diagonal of square is intersect equal at mid point.

Then mid point of diagonal $(4,5)$ and $(12,-3)$ is $\left(\frac{12+4}{2}\right),\left(\frac{5-3}{2}\right)=\left(\frac{16}{2}\right),\left(\frac{5-3}{2}\right)=(8,1)$

Then mid point of diagonal $(12,5)$ and $(14,-3)$ is $\left(\frac{12+4}{2}\right),\left(\frac{5-3}{2}\right)=\left(\frac{16}{2}\right),\left(\frac{5-3}{2}\right)=(8,1)$

Then diagonal intersect at point $(8,1)$.