{"status": "success", "data": {"description_md": "The point $P(a,b)$ in the $xy$-plane is first rotated counterclockwise by $90^\\circ$ around the point $(1,5)$ and then reflected about the line $y = -x$. The image of $P$ after these two transformations is at $(-6,3)$. What is $b - a ?$\n\n$\\textbf{(A)} ~1 \\qquad\\textbf{(B)} ~3 \\qquad\\textbf{(C)} ~5 \\qquad\\textbf{(D)} ~7 \\qquad\\textbf{(E)} ~9$", "description_html": "<p>The point  <span class=\"katex--inline\">P(a,b)</span>  in the  <span class=\"katex--inline\">xy</span> -plane is first rotated counterclockwise by  <span class=\"katex--inline\">90^\\circ</span>  around the point  <span class=\"katex--inline\">(1,5)</span>  and then reflected about the line  <span class=\"katex--inline\">y = -x</span> . The image of  <span class=\"katex--inline\">P</span>  after these two transformations is at  <span class=\"katex--inline\">(-6,3)</span> . What is  <span class=\"katex--inline\">b - a ?</span> </p>\n<p> <span class=\"katex--inline\">\\textbf{(A)} ~1 \\qquad\\textbf{(B)} ~3 \\qquad\\textbf{(C)} ~5 \\qquad\\textbf{(D)} ~7 \\qquad\\textbf{(E)} ~9</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 1, "problem_name": "2021 AMC 10B Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/21_amc10B_p10", "prev": "/problem/21_amc10B_p08"}}