Let’s start the solution by calculating the lengths of the opposite sides. It is known that opposite sides in a rectangle are equal to each other.
Let’s apply the formula for this:
AB = √ ((x1 – x2) ^ 2 – (y1 – y2) ^ 2).
Apply for each segment and obtain the lengths of the sides AB = 3√2; CD = 3√2. We got a pair of equal opposite sides.
And AD = BC = 2√2.
A quadrilateral whose opposite sides are equal is a parallelogram, that is, ABCD is a parallelogram.
Let’s find its diagonal AC and BD = √26. They are equal to each other, which means that the quadrilateral is a rectangle.
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