142. Triangle $ABC$ is right-angled with hypotenuse $AB = 8$ units. This triangle is translated by vector $\overrightarrow{AT}$ in the direction of $\overrightarrow{AM}$ ($M$ is the midpoint of $BC$). If the area enclosed between the original and new triangle is $\dfrac{1}{16}$ of the original area, then the magnitude of vector $\overrightarrow{AT}$ is which of the following? (1) $3$ (2) $4$ (3) $\dfrac{1}{3}$ (4) $\dfrac{1}{4}$ \rule{\textwidth}{0.4pt} Workspace %% Page 8 Page 7 Mathematics 121-A
\textbf{142.} Triangle $ABC$ is right-angled with hypotenuse $AB = 8$ units. This triangle is translated by vector $\overrightarrow{AT}$ in the direction of $\overrightarrow{AM}$ ($M$ is the midpoint of $BC$). If the area enclosed between the original and new triangle is $\dfrac{1}{16}$ of the original area, then the magnitude of vector $\overrightarrow{AT}$ is which of the following?
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(1) $3$ \hfill (2) $4$ \hfill (3) $\dfrac{1}{3}$ \hfill (4) $\dfrac{1}{4}$
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