Question 1079613
Graph:


<img src = "https://i.imgur.com/F9Q4oSf.png">


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


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Slope of AB


{{{m = (y[2] - y[1])/(x[2] - x[1])}}}


{{{m = (-1 - 5)/(-3 - 6)}}}


{{{m = (-6)/(-9)}}}


{{{m = 2/3}}}


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Slope of BC


{{{m = (y[2] - y[1])/(x[2] - x[1])}}}


{{{m = (-4 - (-1))/(-1 - (-3))}}}


{{{m = -3/2}}}


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Slope of CD


{{{m = (y[2] - y[1])/(x[2] - x[1])}}}


{{{m = (2 - (-4))/(8 - (-1))}}}


{{{m = (6)/(9)}}}


{{{m = 2/3}}}


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Slope of DA


{{{m = (y[2] - y[1])/(x[2] - x[1])}}}


{{{m = (5 - 2)/(6 - 8)}}}


{{{m = (3)/(-2)}}}


{{{m = -3/2}}}


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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: <font size=4 color=red>The figure is a rectangle</font>