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Classifying parallelograms in the coordinate planePart A: Slope of RSSlope of side adjacent to RSPart B: Length of RSLength of side adjacent to RSFrom parts (a) and (b), what can we conclude about parallelogramPORS? Check all that apply.O PORS is a rectangle.O PQRS is a rhombus.O PQRS is a square.- PORS is none of these.

Classifying Parallelograms In The Coordinate PlanePart A Slope Of RSSlope Of Side Adjacent To RSPart B Length Of RSLength Of Side Adjacent To RSFrom Parts A And class=

Answer :

Given:

PQRS has vertices P(6, -6), Q(1, 1), R(-6, 6) and S(-1, -1)

Required: Complete each part

Explanation:

Part A:

By using the two point formula,

[tex]\begin{gathered} \text{ Slope of RS =}\frac{-1-6}{-1-(-6)} \\ =-\frac{7}{5} \end{gathered}[/tex]

Sides adjacent to RS are RQ ans SP.

Slope of RQ

[tex]\begin{gathered} =\frac{6-1}{-6-1} \\ =-\frac{5}{7} \end{gathered}[/tex]

Part B:

Length of RS

[tex]\begin{gathered} =\sqrt{(-6-(-1))^2+(6-(-1))^2} \\ =\sqrt{25+49} \\ =\sqrt{74} \end{gathered}[/tex]

Length of side adjacent to RS

[tex]\begin{gathered} RQ=\sqrt{(-6-1)^2+(6-1)^2} \\ =\sqrt{49+25} \\ =\sqrt{74} \end{gathered}[/tex]

(c) It is a parallelogram with all sides equal. Hence it is a rhombus.

Final Answer:

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