2020 AMC 12A Problems/Problem 6

Line $\ell$ in the coordinate plane has the equation $3x - 5y + 40 = 0$ . This line is rotated $45^{\circ}$ counterclockwise about the point $(20, 20)$ to obtain line $k$ . What is the $x$ -coordinate of the $x$ -intercept of line $k?$

$\textbf{(A) } 10 \qquad \textbf{(B) } 15 \qquad \textbf{(C) } 20 \qquad \textbf{(D) } 25 \qquad \textbf{(E) } 30$

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2020 AMC 12A Problems/Problem 6