Question

A rhombus, which is a quadrilateral with 4 equal sides, is plotted on the coordinate plane. The coordinates of the vertices are: (5,3), (2,-1), (-3,-1), (0,3). How long is each side of the rhombus?

Answer 1

C=5
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Answer 2

If it is a rhombus then you know each side is the same length, so only have to work out one side. To do this you have to use Pythagoras' theorem (a^2 + b^2 = c^2)
So take two sets of coordinates, for example, (0,3) and (5,3), a and b represent the height difference and the length difference. Therefore (5-0)^2 + (3-3)^2 = c^2
c^2 = 25
c = 5 , which would be the side of the rhombus