Problem

Which choice correctly tests the claim that \(A(0,0)\), \(B(4,0)\), \(C(5,3)\), and \(D(1,2)\), in order, form a parallelogram?

Source coordinate plane: Quadrilateral ABCD has vertices A(0,0), B(4,0), C(5,3), and D(1,2); no slopes or parallelogram conclusion are shown.

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What this problem is really about

A disproof needs only one exact violation of a necessary condition, so look for the shortest decisive measurement instead of checking every property. For a parallelogram claim, compare an opposite-side pair with consistent slope subtraction; if that required parallel relationship fails, no later measurement can rescue the classification.

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claim = true; measurements = mAB=0 and mCD=1/4; condition assessment = both slopes are nonnegative and therefore parallel; conclusion = ABCD is a parallelogram

claim = false; measurements = mAB=0 and mCD=0; condition assessment = opposite sides AB and CD are parallel; conclusion = ABCD is not a parallelogram

claim = false; measurements = mAB=0 and mCD=1/4; violated condition = opposite sides AB and CD are not parallel; conclusion = ABCD is not a parallelogram

claim = false; measurements = mAB=0 and mCD=1/4; condition assessment = opposite sides AB and CD are not parallel; conclusion = ABCD is not a parallelogram

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Which choice correctly tests the claim that \(A(0,0)\), \(B(4,0)\), \(C(5,3)\), and \(D(1,2)\), in order, form a parallelogram?

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