SOLUTION: Hi. How would I use the distance, midpoint and slope formula to find where a point should go to make a parallelogram? Because on this homework it shows point A(7,12) B(15,4) C(9,2)

Question 113923: Hi. How would I use the distance, midpoint and slope formula to find where a point should go to make a parallelogram? Because on this homework it shows point A(7,12) B(15,4) C(9,2) D(3,5) The question is to move Point B so that it makes a parallelogram. How would I know where to move it? Thank You for your help!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
How would I use the distance, midpoint and slope formula to find where a point should go to make a parallelogram? Because on this homework it shows point A(7,12) B(15,4) C(9,2) D(3,5) The question is to move Point B so that it makes a parallelogram. How would I know where to move it? Thank You for your help!
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Plot the points A, C, and D.
AB has to be parallel to DC.
The slope of DC = (2-5)/(9-3) = -3/6 = -1/2
So the slope of AB as to be -1/2.
AB also has to pass thru A(7,12)
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Line AB has the form y=mx+b where y = 12 when x=7, and m = -1/2
12 = (-1/2)7 + b
b = 24/2 +7/2 = 31/2
AB has equation y = (-1/2)x+31/2
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Line AD has slope (12-5)/(7-3) = 7/4
Line CB must has the same slope and must pass thru C(9,2)
2 = (7/4)9 + b
b = 8/4 -63/4 = -55/4
CB has equation y = (7/4)x-55/4
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B is at the intersection of AB and CB.
(-1/2)x + (31/2) = (7/4)x-(55/4)
(9/4)x = 117/4
x = 13
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Substitute into y = (-1/2)x+31/2 to solve for y:
y = (-1/2)(13)+(31/2)
y = -13/2 + 31/2
y = 9
------------
Coordinates of B need to be (13,9)
==============
Cheers,
Stan H.

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