Problem 109

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Problem 109: (2007 AMC 12a, 19)

Triangles $ABC$ and $ADE$ have areas $2007$ and $7002,$ respectively, with $B = (0,0),$ $C = (223,0),$ $D = (680,380),$ and $E = (689,389).$ What is the sum of all possible $x$ coordinates of $A$? $\mathrm{(A)}\ 282 \qquad$ $ \mathrm{(B)}\ 300 \qquad$ $ \mathrm{(C)}\ 600 \qquad$ $ \mathrm{(D)}\ 900 \qquad$ $ \mathrm{(E)}\ 1200$

Solution

Exercise 109: Solution

Triangles $ABC$ and $ADE$ have areas $1000$ and $3000$, respectively, with $B=(0,0)$, $C=(100,0)$, $D=(300,200)$, and $E=(310,210)$. What is the sum of all possible $x$-coordinates of $A$?

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