Find the equations of the diagonals of a rectangle whose sides are: x = –1, x = 4, y = –1 and y = 2.

From figure,

The lines intersect at point I, J, K and L.

By two point formula,

Equation of line : $y - y$1 = \dfrac{y2 - y1}{x2 - x1}(x - x1)

Equation of diagonal IK is

$\Rightarrow y - 2 = \dfrac{-1 - 2}{4 - (-1)}[x - (-1)] \\[1em] \Rightarrow y - 2 = -\dfrac{3}{5}[x + 1] \\[1em] \Rightarrow 5(y - 2) = -3[x + 1] \\[1em] \Rightarrow 5y - 10 = -3x -3 \\[1em] \Rightarrow 5y + 3x -10 + 3 = 0 \\[1em] \Rightarrow 3x + 5y - 7 = 0 \\[1em] \Rightarrow 3x + 5y = 7.$

Equation of diagonal LJ is

⇒ y - (-1) = $\dfrac{2 - (-1)}{4 - (-1)}$ [x - (-1)]

⇒ y - (-1) = $\dfrac{3}{5}$ [x - (-1)]

⇒ 5(y + 1) = 3[x + 1]

⇒ 5y + 5 = 3x + 3

⇒ 5y − 3x + 5 − 3 = 0

⇒ 5y - 3x + 2 = 0

⇒ 3x - 5y = 2.

Hence, equation of diagonals are 3x - 5y = 2 and 3x + 5y = 7.