Question 1197771
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1/2 = 0.5
7/2 = 3.5


We have a triangle with unknown vertices. 
The midpoints of this triangle are
A = (0, -3)
B = (-0.5, 3.5)
C = (-3.5, 0.5)


The motion from B to C is "down 3, left 3"
We'll follow that motion pattern when starting at point A.


Start at A(0,-3) and move down 3, left 3 to arrive at (-3,-6) which is one of the vertices of the triangle. Label this as point D.


D = (-3,-6)


Notice that ABCD is a parallelogram.
*[illustration Screenshot_108.png]
The motion from A to B is "left 0.5, up 6.5"
Follow this pattern when starting at point C and you should arrive at (-4,7) which I'll call point E.
E = (-4,7)
This is another vertex of the triangle we're after.


The motion from C to A is "right 3.5, down 3.5"
Follow this pattern when starting at point B and you should arrive at (3,0) which I'll call point F.
F = (3,0)


Therefore, triangle DEF has the midpoints A,B,C mentioned.
D = (-3,-6)
E = (-4,7)
F = (3,0)
*[illustration Screenshot_109.png]
Use the midpoint formula to confirm that<ul><li>point A is the midpoint of segment DF</li><li>point B is the midpoint of segment EF</li><li>point C is the midpoint of segment DE</li></ul>I'll let the student perform these confirmations.


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<font color=red>Answers:</font>
(-3,-6)
(-4, 7)
(3, 0)
The order of the points doesn't matter.
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