{"status": "success", "data": {"description_md": "Triangle $OAB$ has $O=(0,0)$, $B=(5,0)$, and $A$ in the first quadrant. In addition, $\\angle ABO=90^\\circ$ and $\\angle AOB=30^\\circ$. Suppose that $OA$ is rotated $90^\\circ$ counterclockwise about $O$. What are the coordinates of the image of $A$? \n\n$\\mathrm{(A)}\\ \\left( - \\frac {10}{3}\\sqrt {3},5\\right)\n\\qquad\n\\mathrm{(B)}\\ \\left( - \\frac {5}{3}\\sqrt {3},5\\right)\n\\qquad\n\\mathrm{(C)}\\ \\left(\\sqrt {3},5\\right)\n\\qquad\n\\mathrm{(D)}\\ \\left(\\frac {5}{3}\\sqrt {3},5\\right)\n\\qquad\n\\mathrm{(E)}\\ \\left(\\frac {10}{3}\\sqrt {3},5\\right)$", "description_html": "<p>Triangle  <span class=\"katex--inline\">OAB</span>  has  <span class=\"katex--inline\">O=(0,0)</span> ,  <span class=\"katex--inline\">B=(5,0)</span> , and  <span class=\"katex--inline\">A</span>  in the first quadrant. In addition,  <span class=\"katex--inline\">\\angle ABO=90^\\circ</span>  and  <span class=\"katex--inline\">\\angle AOB=30^\\circ</span> . Suppose that  <span class=\"katex--inline\">OA</span>  is rotated  <span class=\"katex--inline\">90^\\circ</span>  counterclockwise about  <span class=\"katex--inline\">O</span> . What are the coordinates of the image of  <span class=\"katex--inline\">A</span> ?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ \\left( - \\frac {10}{3}\\sqrt {3},5\\right)\n\\qquad\n\\mathrm{(B)}\\ \\left( - \\frac {5}{3}\\sqrt {3},5\\right)\n\\qquad\n\\mathrm{(C)}\\ \\left(\\sqrt {3},5\\right)\n\\qquad\n\\mathrm{(D)}\\ \\left(\\frac {5}{3}\\sqrt {3},5\\right)\n\\qquad\n\\mathrm{(E)}\\ \\left(\\frac {10}{3}\\sqrt {3},5\\right)</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": "2008 AMC 10B Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc10B_p15", "prev": "/problem/08_amc10B_p13"}}