{"status": "success", "data": {"description_md": "The line segment formed by $A(1, 2)$ and $B(3, 3)$ is rotated to the line segment formed by $A'(3, 1)$ and $B'(4, 3)$ about the point $P(r, s)$. What is $|r-s|$?\n\n$\\textbf{(A) } \\frac{1}{4} \\qquad \\textbf{(B) } \\frac{1}{2} \\qquad \\textbf{(C) } \\frac{3}{4}   \\qquad \\textbf{(D) } \\frac{2}{3} \\qquad   \\textbf{(E) } 1$", "description_html": "<p>The line segment formed by  <span class=\"katex--inline\">A(1, 2)</span>  and  <span class=\"katex--inline\">B(3, 3)</span>  is rotated to the line segment formed by  <span class=\"katex--inline\">A'(3, 1)</span>  and  <span class=\"katex--inline\">B'(4, 3)</span>  about the point  <span class=\"katex--inline\">P(r, s)</span> . What is  <span class=\"katex--inline\">|r-s|</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } \\frac{1}{4} \\qquad \\textbf{(B) } \\frac{1}{2} \\qquad \\textbf{(C) } \\frac{3}{4}   \\qquad \\textbf{(D) } \\frac{2}{3} \\qquad   \\textbf{(E) } 1</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": 3, "problem_name": "2023 AMC 10A Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/23_amc10A_p20", "prev": "/problem/23_amc10A_p18"}}