Use coordinates, distance, and algebra to prove or disprove simple geometric statements.
Use midpoint formula to show diagonals bisect each other
Problem
Calculate the midpoints of diagonals \(A(0,0)\)\(C(6,4)\) and \(B(6,0)\)\(D(0,4)\). Use the results to determine whether the diagonals bisect each other.
Bisection is a shared-midpoint claim, so calculate the midpoint of each diagonal independently rather than averaging all four vertices at once. Compare both coordinates of the results: one common point means that each diagonal passes through the other’s midpoint and cuts it into two equal parts.
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