SOLUTION: The midpoints of a triangle are (3,-1) (4,3) and (0,5). Find coordinates for the vertices of the triangle...

Question 147597: The midpoints of a triangle are (3,-1) (4,3) and (0,5). Find coordinates for the vertices of the triangle...
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Let the end points with midpoint (3,-1) be (a,b) and (c,d)
Let the end points with midpoint (4,3) be (c,d) and (e,f)
Then the end points with midpoint (0,5) are (e,f) and (a,b)
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Note: Each coordinate of a midpoint is the average of the corresponding
coordinates of the end points.
For example (a+c)/2 = 3 and (b+d)/2 = -1
Therefore a+c = 6 and b+d = -1
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Using that same idea on the three midpoints you get 6 equations with 6 variables:
a + 0 + c + 0 + 0 + 0 = 6
a + 0 + 0 + 0 + e + 0 = 0
0 + 0 + c + 0 + e + 0 = 8
0 + b + 0 + d + 0 + 0 = -2
0 + 0 + 0 + d + 0 + f = 6
0 + b + 0 + 0 + 0 + f = 10
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Solve that system of equations using any method to get:
a = -1
b = 1
c = 7
d = -3
e = 1
f = 9
============
Cheers,
Stan H.

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