Use coordinates to prove simple geometric theorems, including simple circle theorems.
Disprove a claim with a specified coordinate calculation
Problem
Disprove the claim that \(ABCD\) is a rectangle in the stated vertex order. Calculate slopes \(\text{mAB}\) and \(\text{mBC}\) from the supplied coordinates, test whether the adjacent sides are perpendicular, identify the failed rectangle condition, and state the counterconclusion.
Disproving a classification requires only one exact failure of a necessary condition. We’ll name the adjacent-side right-angle requirement for a rectangle, compute both adjacent directions from the coordinates, apply the correct perpendicularity test, and state precisely how the failed angle condition defeats the original claim.
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