Question

Find the equation of the diagonals of a rectangle whose sides are x = −1, x = 2, y = −2, and y = 6.

Answer 1

Given values:

• x = −1 and y = −2 → A(−1, −2)
• x = 2 and y = −2 → B(2, −2)
• x = 2 and y = 6 → C(2, 6)
• x = −1 and y = 6 → D(−1, 6)

⇒ The diagonal joining A(−1, −2) and C(2, 6) is found using the two-point formula:

`(y - y_1)/(x - x_1) = (y_2 - y_1)/(x_2 - x_1)`

`(y - (-2))/(x - (-1)) = (6 - (-2))/(2 - (-1))`

`(y + 2)/(x + 1) = 8/3`

3(y + 2) = 8(x + 1)

3y + 6 = 8x + 8

∴ 8x − 3y + 2 = 0

⇒ The diagonal joining B(2, −2) and D(−1, 6) is found similarly:

`(y - (-2))/(x - 2) = (6 - (-2))/(-1 - 2)`

`(y + 2)/(x - 2) = 8/-3`

−3(y + 2) = 8(x − 2)

−3y − 6 = 8x − 16

∴ 8x + 3y − 10 = 0

Hence, the equations of the diagonals of a rectangle are 8x − 3y + 2 = 0 and 8x + 3y − 10 = 0.