MathDB
Line Rotation

Source: 2020 AMC 12A #12

January 31, 2020
AMC 12AMC 12 Aanalytic geometryrotationgeometry2020 AMC 12A2020 AMC

Problem Statement

Line \ell in the coordinate plane has the equation 3x5y+40=03x - 5y + 40 = 0. This line is rotated 4545^{\circ} counterclockwise about the point (20,20)(20, 20) to obtain line kk. What is the xx-coordinate of the xx-intercept of line k?k?
<spanclass=latexbold>(A)</span>10<spanclass=latexbold>(B)</span>15<spanclass=latexbold>(C)</span>20<spanclass=latexbold>(D)</span>25<spanclass=latexbold>(E)</span>30<span class='latex-bold'>(A) </span> 10 \qquad <span class='latex-bold'>(B) </span> 15 \qquad <span class='latex-bold'>(C) </span> 20 \qquad <span class='latex-bold'>(D) </span> 25 \qquad <span class='latex-bold'>(E) </span> 30