Question

Find the equations of the diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y =1. 

Answer 1

Suppose ABCD is the reequired square from by four vertices having diagonals AC and BD.
The equation of the diagonal AC is given by

\[x - 0 = \left( y - 0 \right)\frac{1 - 0}{1 - 0}\]

\[ \Rightarrow x = y\]

The equation of the diagonal BD is given by

\[x - 1 = \left( y - 0 \right)\frac{1 - 0}{0 - 1}\]

\[ \Rightarrow x - 1 = - y\]

\[ \Rightarrow x + y = 1\]