{"status": "success", "data": {"description_md": "Which one of the following rigid transformations (isometries) maps the line segment $\\overline{AB}$ onto the line segment $\\overline{A'B'}$ so that the image of $A(-2,1)$ is $A'(2,-1)$ and the image of $B(-1,4)$ is $B'(1,-4)?$\n\n$\\textbf{(A) }$ reflection in the $y$-axis\n\n$\\textbf{(B) }$ counterclockwise rotation around the origin by $90^{\\circ}$\n\n$\\textbf{(C) }$ translation by $3$ units to the right and $5$ units down\n\n$\\textbf{(D) }$ reflection in the $x$-axis\n\n$\\textbf{(E) }$ clockwise rotation about the origin by $180^{\\circ}$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Which one of the following rigid transformations (isometries) maps the line segment  <span class=\"katex--inline\">\\overline{AB}</span>  onto the line segment  <span class=\"katex--inline\">\\overline{A'B'}</span>  so that the image of  <span class=\"katex--inline\">A(-2,1)</span>  is  <span class=\"katex--inline\">A'(2,-1)</span>  and the image of  <span class=\"katex--inline\">B(-1,4)</span>  is  <span class=\"katex--inline\">B'(1,-4)?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }</span>  reflection in the  <span class=\"katex--inline\">y</span> -axis</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(B) }</span>  counterclockwise rotation around the origin by  <span class=\"katex--inline\">90^{\\circ}</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(C) }</span>  translation by  <span class=\"katex--inline\">3</span>  units to the right and  <span class=\"katex--inline\">5</span>  units down</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(D) }</span>  reflection in the  <span class=\"katex--inline\">x</span> -axis</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(E) }</span>  clockwise rotation about the origin by  <span class=\"katex--inline\">180^{\\circ}</span> </p>&#10;<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": 2, "problem_name": "2019 AMC 12B Problem 3", "can_next": true, "can_prev": true, "nxt": "/problem/19_amc12B_p04", "prev": "/problem/19_amc12B_p02"}}