AMC 12B 2024 (Problem 15)

Coordinate GeometryMedium

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

\text{(A)}\;\log_2\frac{\sqrt{3}}{7}

\text{(B)}\;\log_2\frac{3}{\sqrt{7}}

\text{(C)}\;\log_2\frac{7}{\sqrt{3}}

\text{(D)}\;\log_2\frac{11}{\sqrt{7}}

\text{(E)}\;\log_2\frac{11}{\sqrt{3}}