If (2, –2) and (5, 2) are two consecutive vertices of a square, then the length of each side of the square will be:

Correct option is A

Given:

Two consecutive vertices of a square: (2,−2) and (5,2)

Formula Used:

The distance between two points (x₁,y₁) and (x₂,y₂) is:

​$$\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$​​

For a square, the distance between two consecutive vertices is equal to the side length.

Solution:

Apply the distance formula:

​$$\text{Side length} = \sqrt{(5 - 2)^2 + (2 - (-2))^2}$$​

Side length =$$\sqrt{(3)^2 + (4)^2}$$​​

​$$\text{Side length} = \sqrt{9 + 16} = \sqrt{25} = 5$$

Option (a) is right.