Use coordinates, distance, and algebra to prove or disprove simple geometric statements.
Choose the best coordinate method for a geometric claim
Problem
State the coordinate quantity to calculate and compare when testing whether \(\text{both}~\text{pairs}\) of opposite sides of a quadrilateral are parallel.
Big Picture
What this problem is really about
Match the geometric verb to the coordinate invariant it describes before calculating anything: length claims use distance, bisection claims use midpoints, and parallel or perpendicular claims use direction. For a quadrilateral, apply that invariant to the required side pairs and remember that vertical directions need direct classification instead of numerical slopes.
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