How do you find the side lengths of a square when only given the coordinates on the graph? Coordinates are (0,0), (5,2), (3,7), and (-2, 5).

Answer 1

Each side length is the distance between its vertices (the given coordinates).

So find the distance (d = sqrt[ (x₂-x₁)²+(y₂-y₁)² ] )

between (0,0) and (5,2)

d = sqrt(5²+2²) = √29

between (5,2) and (3,7)

d = sqrt( (-2)²+ 5²) = √29

between (3,7) and (-2,5)

d = sqrt( (-5)² + (-2)² ) = √29

between (-2,5) and (0,0)

d = sqrt ( 2² + (-5)²) = √29

Since all of these distances are √29, the answer is that the

length of one of the sides is √29