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If (-1, 2) and (2, -1) are two opposite vertices of a square, what is the perimeter of the square?

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The sides length of the square is 3 units, then the perimeter of the square is 12 units.

What is a square?

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a square, opposite sides are parallel and all sides are equal and each angle is 90 degrees. And its diagonals are also equal and intersect at the mid-point.

If (-1, 2) and (2, -1) are two opposite vertices of a square, then the perimeter of the square will be

The other two vertices of the square will be

(-1, -1) and (2, 2)

Then the distance between the points (2, 2) and (2, -1) will be

$$\rm D = \sqrt{(2-2)^2+ (-1-2)^2}\\\\D = \sqrt{3^2}\\\\D = 3$$

Then the perimeter of the square will be

Perimeter = 4 × 3

Perimeter = 12 units