Problem

Verify that the ordered vertices \(W(-2,-1)\), \(X(2,-1)\), \(Y(2,5)\), \(Z(-2,5)\) form rectangle \(WXYZ\). Give \(\text{all}~\text{four}~\text{side}~\text{slopes}\), \(\text{both}~\text{opposite}\text{-}\text{side}~\text{parallel}~\text{checks}\), an adjacent-side perpendicular check, and the conclusion.

Source coordinate plane: Quadrilateral WXYZ has vertices W(-2,-1), X(2,-1), Y(2,5), and Z(-2,5); no slopes or rectangle conclusion are shown.

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side slopes = WX 0, XY vertical, YZ 0, ZW vertical; parallel checks = WX∥YZ and XY∥ZW; perpendicular check = WX⊥XY (horizontal/vertical); conclusion = WXYZ is a rectangle

side slopes = WX 0, XY vertical, YZ 0, ZW vertical; parallel checks = WX∥YZ and XY∥ZW; perpendicular check = WX⊥XY because horizontal and vertical lines are perpendicular; conclusion = every parallelogram is a rectangle

side slopes = WX 0, XY vertical, YZ 0, ZW vertical; parallel checks = WX∥YZ and XY∥ZW; perpendicular check = 0·vertical is not -1; conclusion = WXYZ is not a rectangle

side slopes = WX 0, XY vertical, YZ 0, ZW vertical; parallel checks = WX∥XY and YZ∥ZW; perpendicular check = WX⊥XY because horizontal and vertical lines are perpendicular; conclusion = WXYZ is a rectangle

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