SOLUTION: Given the coordinates W(-7,-2) X(-2,5) Y(5,0) Z(0,-7) Prove that wxyz is a parallelogram find the slopes of each side. Is wxyz a special type of parallelogram? Explain

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Question 717700: Given the coordinates
W(-7,-2)
X(-2,5)
Y(5,0)
Z(0,-7)
Prove that wxyz is a parallelogram find the slopes of each side. Is wxyz a special type of parallelogram? Explain
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Use the slope formula to calculate the slopes of the four segments WX, XY, YZ, and ZW.



where and are the coordinates of the given points.

If the slope of WX is equal to the slope of YZ and the slope of XY is equal to the slope of ZW, then the opposite sides of the quadrilateral are parallel to each other and then by definition the quadrilateral is a parallelogram.

If the slope of WX (and YZ, presuming a parallelogram) is the negative reciprocal of the slope of XY and/or ZW, then the adjacent sides are perpendicular and the quadrilateral is at least a rectangle.

Use the distance formula to calculate the measure of segments WX and XY:



If two adjacent sides are equal in measure, then given perpendicular adjacent sides the quadrilateral is a square and a rhombus. If not perpendicular adjacent sides then just a rhombus.

John

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