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) (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
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Slope of BC
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Slope of CD
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Slope of DA
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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
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