SOLUTION: Given that ABCD is a straight line. B is the midpoint of AC and C is the midpoint of BD. If coordinates A and D are (-14,2) and (-2, 2) respectively. Find the coordinates of A and

Algebra ->  Length-and-distance -> SOLUTION: Given that ABCD is a straight line. B is the midpoint of AC and C is the midpoint of BD. If coordinates A and D are (-14,2) and (-2, 2) respectively. Find the coordinates of A and       Log On


   

Question 981245: Given that ABCD is a straight line. B is the midpoint of AC and C is the midpoint of BD. If coordinates A and D are (-14,2) and (-2, 2) respectively. Find the coordinates of A and C.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
From the midpoint formula,
x%5BB%5D=%28x%5BA%5D%2Bx%5BC%5D%29%2F2
y%5BB%5D=%28y%5BA%5D%2By%5BC%5D%29%2F2
and
x%5BC%5D=%28x%5BB%5D%2Bx%5BD%5D%29%2F2
y%5BC%5D=%28y%5BB%5D%2By%5BD%5D%29%2F2
.
.
1.2x%5BB%5D=-14%2Bx%5BC%5D
2.2y%5BB%5D=2%2By%5BC%5D
and
3.2x%5BC%5D=x%5BB%5D-2
4.2y%5BC%5D=y%5BB%5D%2B2
So solving the x equations (1 & 3) by substituting,
2%282x%5BB%5D%2B14%29=x%5BB%5D-2
4x%5BB%5D%2B28=x%5BB%5D-2
3x%5BB%5D=-30
x%5BB%5D=-10
and
2%28-10%29=-14%2Bx%5BC%5D
-20=-14%2Bx%5BC%5D%7D%7D%0D%0A%7B%7B%7Bx%5BC%5D=-6
Then solving the y equations (2 & 4) similarly,
2%282y%5BC%5D-2%29=2%2By%5BC%5D
4y%5BC%5D-4=2%2By%5BC%5D
3y%5BC%5D=6
y%5BC%5D=2
and
2%282%29=y%5BB%5D%2B2
y%5BB%5D=2
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.
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B:(-10,2)
C:(-6,2)
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