# Choose the correct answer from the given four options. Equations of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are

$\begin {array} {1 1} (A)\;y = x, y + x = 1 & \quad (B)\;y = x, x + y = 2 \\ (C)\;2y = x, y + x =\large\frac{1}{3} & \quad (D)\;y = 2x, y + 2x = 1 \end {array}$

Toolbox:
• Equation of line whose join of points is $(x_1,y_1)$ and $(x_2, y_2)$ is $\large\frac{y-y_1}{y_2-y_1}$$=\large\frac{x-x_1}{x_2-x_1} Step 1 : The equation of the square formed by the lines are x=0, y=0, x=1 \: and \: y=1 respectively. Hence the vertices of the square are 0(0,0), A(1,0), B (1,1), C (0,1) respectively Hence the equation of the diagonals 0B is \large\frac{y-y_1}{y_2-y_1}$$= \large\frac{x-x_1}{x_2-x_1}$
(i.e) $\large\frac{y-0}{1-0}$$=\large\frac{x-0}{1-0} \Rightarrow y=x--------(1) equation of the diagonal AC is \large\frac{y-0}{1-0}$$ = \large\frac{x-1}{0-1}$
$\Rightarrow -y=x-1$
$\Rightarrow x+y=1$
Hence 'A' is the correct answer.