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Question 132035: Segment AD has a midpoint B, BD has a midpoint C. If A has coordinates (-5, 4) and C has coordinates (10, 11), what are the coordinates of B and D?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Segment AD has a midpoint B, BD has a midpoint C. If A has coordinates (-5, 4) and C has coordinates (10, 11), what are the coordinates of B and D?
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That's a pretty messy problem, but doable.
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Draw the picture so you can follow what is happening.
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Label point D as (a,b)
Label point B as (x,y)
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EQUATIONS:
Since C is the midpoint of BD
x+a = 2*10
y+b = 2*11
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Since B is the midpoint of AD
a-5=2x
b+4=2y
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Look at these two equations:
x+a = 20
2x-a = -5
Add them to solve for x:
3x = 15
x = 5
Substitute to solve for "a":
5+a=20
a= 15
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Look at these two equations:
y+b = 22
2y-b=4
Add to solve for y:
3y = 26
y = 26/3
Substitute to solve for "b":
(26/3)+b = (66/3)
b = 40/3
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Coordinates:
(a,b) = (15,40/3)
(x,y) = (5,26/3)
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Cheers,
Stan H.
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