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September 1st, 2018, 03:46 PM   #1
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Totally confusing:coordinate geometry

Since I saw this question, I'm totally confused, but I know it is my inability to think deeply. I need help once again. I need full solution please... Need to wake up in the middle of the night and post to forum... Help me!!!!

The points D(2,1), E(1,5) and F(-6,-1) are the midpoints of the sides AC, AB and BC respectively of triangle ABC.
Find the coordinates of ABC.

Last edited by skipjack; September 1st, 2018 at 06:18 PM.
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September 1st, 2018, 04:00 PM   #2
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Quote:
Originally Posted by Harmeed View Post
Since I saw this question, I'm totally confused, but I know it is my inability to think deeply. I need help once again. I need full solution please... Need to wake up in the middle of the night and post to forum... Help me!!!!

The points D(2,1), E(1,5) and F(-6,-1) are the midpoints of the sides AC, AB and BC respectively of triangle ABC.
Find the coordinates of ABC.
$\begin{align*}
&A+C = 2D = (4,2) \\ \\

&A+B = 2E = (2,10) \\ \\

&B+C = 2F = (-12,-2)

\end{align*}$

and solve for $A,~B,~C$
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Last edited by skipjack; September 1st, 2018 at 06:18 PM.
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September 1st, 2018, 06:26 PM   #3
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A = (A + C)/2 + (A + B)/2 - (B + C)/2 = D + E - F = D(2,1) + E(1,5) - F(-6,-1) = (9, 7), etc.
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