Question

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

Answer 1

We have,

$x=0,y=0,x=1,y=1$

Now,

Let

$O(x_1,y_1)=(0,0)$

$A(x_2,y_2)=(1,0)$

$B(x_3,y_3)=(1,1)$

$C(x_3,y_3)=(0,1)$

Are the vertices of square.

Now,

Equation of the straight line passing through the points $(x_1,y_1)$ and $(x_2,y_2)$ is,

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Now, equation of diagonal OB is

$y-0=\frac{1-0}{1-0}(x-0)$

$\Rightarrow y=x$

Now, equation of diagonal AC is

$y-0=\frac{1-0}{0-1}(x-1)$

$\Rightarrow y=-(x-1)$

$\Rightarrow y=-x+1$

$\Rightarrow x+y+1=0$

Hence, this is the answer.