Question

ABCD is a rectangle with its vertices at (2, –2), (8, 4), (4, 8) and (–2, 2) taken in order. Length of its diagonal is ______.

Options

• `4sqrt(2)`

• `6sqrt(2)`

• `4sqrt(26)`

• `2sqrt(26)`

Answer 1

ABCD is a rectangle with its vertices at (2, –2), (8, 4), (4, 8) and (–2, 2) taken in order. Length of its diagonal is `underlinebb(2sqrt(26))`.

Explanation:

Given, A(2, –2), В(8, 4), С(4, 8), D(–2, 2)

By using distance formula,

AC = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`

= `sqrt((4 - 2)^2 + (8 - (-2))^2`

= `sqrt((2)^2 + (10)^2)`

= `sqrt(4 + 100)`

= `sqrt(104)`

= `2sqrt(26)`