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Question 283748: A square has vertices U(-2,1), V(2,3), W(4,-1) and X(0,-3). Verify that the diagonals perpendicularly bisect each other.
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! The four points can be plotted:
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The diagonals are defined by the points: U,W and V,X.
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We need to solve for a line going through the first pair of points
U (-2,1)
W (4,-1)
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y = mx + b
m= (-1-1)/(4-(-2))= -2/6 = -1/3
y = -1/3x + b
We can solve for 'b' by plugging in the points we know.
1 = -1/3*(-2 ) + b
b = 1/3
or
-1 = -1/3*4 +b
b = 1/3
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y=-1/3x + 1/3 defines the equation for the first diagonal.
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Then we need to find the equation for the line going through the other two points
V (2,3)
X (0,-3)
m= (-3-3)/(0-2) = -6/-2 = 6/2 = 3
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At this point we know the diagonals are perpendicular because, by definition, the slopes of perpendicular lines are the negative reciprocal.
-1/3 is the negative reciprocal of 3.
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But we can press on to continue to define the second equation...
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-3 = 3(0) + b
b = -3
or
3 = 3(2) + b
b = -3
y = 3x -3
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Then a graph will illustrate they are perpendicular.
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