SOLUTION: graph a quadrilateral with points of A(6,5), B(-3,-1), C(-1,-4), D(8,2) what type of quadrilateral is ABCD? Use slope to justify my answer

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Question 1079613: graph a quadrilateral with points of A(6,5), B(-3,-1), C(-1,-4), D(8,2)
what type of quadrilateral is ABCD? Use slope to justify my answer
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Graph:



Let's find the slopes of the four sides (AB, BC, CD, DA)

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Slope of AB

m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29

m+=+%28-1+-+5%29%2F%28-3+-+6%29

m+=+%28-6%29%2F%28-9%29

m+=+2%2F3

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Slope of BC

m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29

m+=+%28-4+-+%28-1%29%29%2F%28-1+-+%28-3%29%29

m+=+-3%2F2

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Slope of CD

m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29

m+=+%282+-+%28-4%29%29%2F%288+-+%28-1%29%29

m+=+%286%29%2F%289%29

m+=+2%2F3

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Slope of DA

m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29

m+=+%285+-+2%29%2F%286+-+8%29

m+=+%283%29%2F%28-2%29

m+=+-3%2F2

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In summary so far, we have

Slope of AB = 2/3

Slope of BC = -3/2

Slope of CD = 2/3

Slope of DA = -3/2

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Notice how the opposite sides have equal slopes (AB and CD have same slope; BC and DA have same slope). This means we have parallel opposite sides.

Parallel lines have equal slopes.

So this figure is a parallelogram.

More specifically this figure is a rectangle because the sides are perpendicular. How do we know this? Because the product of the non-equal adjacent slopes is -1

For instance, (slope of AB)*(slope of BC) = (2/3)*(-3/2) = -1. This particular example shows how AB is perpendicular to BC.

Since the adjacent sides are perpendicular, four right angles form to have this figure be a rectangle.
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Final Answer: The figure is a rectangle