Question

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

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

$$\begin{gathered} x-0=\left(y-0\right)\frac{1-0}{1-0} \\ \Rightarrow x=y \end{gathered}$$
The equation of the diagonal BD is given by

$$\begin{gathered} x-1=\left(y-0\right)\frac{1-0}{0-1} \\ \Rightarrow x-1=-y \\ \Rightarrow x+y=1 \end{gathered}$$