Question

It (2, –2) and (5, 2) are opposite vertices of a square, then the length of the side of the square is ______.

Answer 1

It (2, –2) and (5, 2) are opposite vertices of a square, then the length of the side of the square is `underlinebb(5sqrt(2))`.

Explanation:

1. The distance between the opposite vertices is the diagonal:

`d = sqrt((5 - 2)^2 + (2 - (-2))^2)` 

= `sqrt(3^2 + 4^2)`

= 5

2. For a square,

Side = `"Diagonal"/sqrt(2)`

So side = `5/sqrt(2)`

= `(5sqrt(2))/2 ≈ 3.535`