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MathNet 2024-part-06 — 165 problems (EN–VI) Question 10

Math Olympiad Vault · MathNet 2024-part-06 — 165 problems (EN–VI)

Question 10

A triangle in the coordinate plane has vertices $A(\log_2 1, \log_2 2)$, $B(\log_2 3, \log_2 4)$, and $C(\log_2 7, \log_2 8)$. What is the area of $\triangle ABC$?
(A) $\log_2 \frac{\sqrt{3}}{7}$ (B) $\log_2 \frac{3}{\sqrt{7}}$ (C) $\log_2 \frac{7}{\sqrt{3}}$ (D) $\log_2 \frac{11}{\sqrt{7}}$ (E) $\log_2 \frac{11}{\sqrt{3}}$