// Numbas version: finer_feedback_settings
{"name": "Create a JSXGraph diagram using JessieCode: Three triangle centres lie on a line", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Create a JSXGraph diagram using JessieCode: Three triangle centres lie on a line", "tags": [], "metadata": {"description": "<p>This question demonstrates how to construct a JSXGraph diagram using JessieCode.</p>\n<p>The construction shows a triangle and its orthocentre, circumcentre and centroid. They are always collinear. You can move the vertices of the triangle.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>{triangle_diagram}</p>\n<p>This diagram was created using the following JessieCode:</p>\n<pre>jessiecode(<br/>&nbsp; 600,600,<br/>&nbsp; \"\"\"<br/>&nbsp;&nbsp;&nbsp; A = point(-2,-2);<br/>&nbsp;&nbsp;&nbsp; B = point(2,-2);<br/>&nbsp;&nbsp;&nbsp; C = point(1,2);<br/>&nbsp; <br/>&nbsp;&nbsp;&nbsp; circumcenter = circumcenter(A,B,C) &lt;&lt; name: \"circumcenter\" &gt;&gt;;<br/>&nbsp;&nbsp;&nbsp; circle(A,B,C) &lt;&lt; strokeOpacity: 0.3 &gt;&gt;;<br/>&nbsp; <br/>&nbsp;&nbsp;&nbsp; side_a = segment(B,C) &lt;&lt; visible: false &gt;&gt;;<br/>&nbsp;&nbsp;&nbsp; side_b = segment(A,C) &lt;&lt; visible: false &gt;&gt;;<br/>&nbsp;&nbsp;&nbsp; side_c = segment(B,A) &lt;&lt; visible: false &gt;&gt;;<br/>&nbsp; <br/>&nbsp;&nbsp;&nbsp; polygon(A,B,C);<br/>&nbsp;&nbsp; &nbsp;<br/>&nbsp;&nbsp;&nbsp; M_a = midpoint(B,C) &lt;&lt; visible: false &gt;&gt;;<br/>&nbsp;&nbsp;&nbsp; M_b = midpoint(A,C) &lt;&lt; visible: false &gt;&gt;;<br/>&nbsp;&nbsp;&nbsp; M_c = midpoint(B,A) &lt;&lt; visible: false &gt;&gt;;<br/>&nbsp; <br/>&nbsp;&nbsp;&nbsp; median_a = line(A,M_a) &lt;&lt; dash: 4, color: \"gray\", strokeOpacity: 0.3 &gt;&gt;;<br/>&nbsp;&nbsp;&nbsp; median_b = line(B,M_b) &lt;&lt; dash: 4, color: \"gray\", strokeOpacity: 0.3 &gt;&gt;;<br/>&nbsp;&nbsp;&nbsp; median_c = line(C,M_c) &lt;&lt; dash: 4, color: \"gray\", strokeOpacity: 0.3 &gt;&gt;;<br/>&nbsp;&nbsp; &nbsp;<br/>&nbsp;&nbsp;&nbsp; centroid = intersection(median_a,median_b) &lt;&lt; name: \"centroid\" &gt;&gt;;<br/>&nbsp; <br/>&nbsp;&nbsp;&nbsp; p_a = perpendicular(side_a,A) &lt;&lt; dash: 1, color: \"gray\", strokeOpacity: 0.3 &gt;&gt;;<br/>&nbsp;&nbsp;&nbsp; p_b = perpendicular(side_b,B) &lt;&lt; dash: 1, color: \"gray\", strokeOpacity: 0.3 &gt;&gt;;<br/>&nbsp;&nbsp;&nbsp; p_c = perpendicular(side_c,C) &lt;&lt; dash: 1, color: \"gray\", strokeOpacity: 0.3 &gt;&gt;;<br/>&nbsp; <br/>&nbsp;&nbsp;&nbsp; orthocenter = intersection(p_a,p_b) &lt;&lt; name: \"orthocenter\" &gt;&gt;;<br/>&nbsp; <br/>&nbsp;&nbsp;&nbsp; euler_line = line(orthocenter, centroid);<br/>&nbsp; \"\"\",<br/>&nbsp; [<br/>&nbsp;&nbsp;&nbsp; \"axis\": false<br/>&nbsp; ]<br/>)</pre>", "advice": "", "rulesets": {}, "extensions": ["jsxgraph"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"triangle_diagram": {"name": "triangle_diagram", "group": "Ungrouped variables", "definition": "jessiecode(\n  600,600,\n  \"\"\"\n    A = point(-2,-2);\n    B = point(2,-2);\n    C = point(1,2);\n  \n    circumcenter = circumcenter(A,B,C) << name: \"circumcenter\" >>;\n    circle(A,B,C) << strokeOpacity: 0.3 >>;\n  \n    side_a = segment(B,C) << visible: false >>;\n    side_b = segment(A,C) << visible: false >>;\n    side_c = segment(B,A) << visible: false >>;\n  \n    polygon(A,B,C);\n    \n    M_a = midpoint(B,C) << visible: false >>;\n    M_b = midpoint(A,C) << visible: false >>;\n    M_c = midpoint(B,A) << visible: false >>;\n  \n    median_a = line(A,M_a) << dash: 4, color: \"gray\", strokeOpacity: 0.3 >>;\n    median_b = line(B,M_b) << dash: 4, color: \"gray\", strokeOpacity: 0.3 >>;\n    median_c = line(C,M_c) << dash: 4, color: \"gray\", strokeOpacity: 0.3 >>;\n    \n    centroid = intersection(median_a,median_b) << name: \"centroid\" >>;\n  \n    p_a = perpendicular(side_a,A) << dash: 1, color: \"gray\", strokeOpacity: 0.3 >>;\n    p_b = perpendicular(side_b,B) << dash: 1, color: \"gray\", strokeOpacity: 0.3 >>;\n    p_c = perpendicular(side_c,C) << dash: 1, color: \"gray\", strokeOpacity: 0.3 >>;\n  \n    orthocenter = intersection(p_a,p_b) << name: \"orthocenter\" >>;\n  \n    euler_line = line(orthocenter, centroid);\n  \"\"\",\n  [\n    \"axis\": false\n  ]\n)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["triangle_diagram"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Laura Midgley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18287/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Laura Midgley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18287/"}]}