<p>Distinct points <img alt="$A$" height="13" src="https://latex.artofproblemsolving.com/0/1/9/019e9892786e493964e145e7c5cf7b700314e53b.png" width="13" />, <img alt="$B$" height="12" src="https://latex.artofproblemsolving.com/f/f/5/ff5fb3d775862e2123b007eb4373ff6cc1a34d4e.png" width="14" />, <img alt="$C$" height="12" src="https://latex.artofproblemsolving.com/c/3/3/c3355896da590fc491a10150a50416687626d7cc.png" width="14" />, and <img alt="$D$" height="14" src="https://latex.artofproblemsolving.com/9/f/f/9ffb448918db29f2a72f8f87f421b3b3cad18f95.png" width="17" /> lie on a line, with <img alt="$AB=BC=CD=1$" height="13" src="https://latex.artofproblemsolving.com/8/e/e/8ee42ac86b004fcc822d941be77bddff14611d46.png" width="168" />. Points <img alt="$E$" height="14" src="https://latex.artofproblemsolving.com/f/a/2/fa2fa899f0afb05d6837885523503a2d4df434f9.png" width="16" /> and <img alt="$F$" height="14" src="https://latex.artofproblemsolving.com/a/0/5/a055f405829e64a3b70253ab67cb45ed6ed5bb29.png" width="16" /> lie on a second line, parallel to the first, with <img alt="$EF=1$" height="14" src="https://latex.artofproblemsolving.com/a/4/7/a47e2091638649c63c5133fd16b46968879020b1.png" width="64" />. A triangle with positive area has three of the six points as its vertices. How many possible values are there for the area of the triangle?</p>

Question No: 294

Distinct points $A$ , $B$ , $C$ , and $D$ lie on a line, with $AB=BC=CD=1$ . Points $E$ and $F$ lie on a second line, parallel to the first, with $EF=1$ . A triangle with positive area has three of the six points as its vertices. How many possible values are there for the area of the triangle?

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Tags: Algebra Geometry

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