The given quadrilateral is a rectangle because 2 pairs of sides are equal in length.
How to find the distance between two coordinates?
We are given the coordinates of the quadrilateral as;
W(0, 5), X(-3, 2), Y(0, -4), Z(3, 2).
Now, the formula for distance between two coordinates is;
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Thus;
WX = √[(-3 - 0)² + (2 - 5)²]
WX = 3√2
XY = √[(0 + 3)² + (-4 - 2)²]
XY = 3√5
YZ = √[(2 + 4)² + (3 - 0)²]
YZ = 3√5
ZW = √[(0 - 3)² + (2 - 5)²]
ZW = 3√2
Thus, we can conclude that the given quadrilateral is a rectangle because 2 pairs of sides are equal in length.
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