Math Gold Medalist

Lor

2023 AMC 12A

Problem 6

Points $A$ and $B$ lie on the graph of $y=\log_{2}x$. The midpoint of $\overline{AB}$ is $(6, 2)$. What is the positive difference between the $x$-coordinates of $A$ and $B$?

$\textbf{(A)}~2\sqrt{11}\qquad\textbf{(B)}~4\sqrt{3}\qquad\textbf{(C)}~8\qquad\textbf{(D)}~4\sqrt{5}\qquad\textbf{(E)}~9$

Coordinate Geometry

Logarithm Rules

Quadratic Equation

x1+x2=12

y1+y2=16 -> x1.x2=16

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   Solution