// Numbas version: exam_results_page_options
{"name": "Perpendicular distance between a point and line", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "definition": "switch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [["question-resources/perpdist.ggb", "/srv/numbas/media/question-resources/perpdist.ggb"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Perpendicular distance between a point and line", "tags": [], "metadata": {"description": "<p>Given a point and a line, determine the distance between them.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{show_triangle(applet,debug)}</p>\n<p>Determine the perpendicular distance between point $B$ = ({B[0]}, {B[1]}) and a line passing through point $A$ = ({A[0]}, {A[1]}) &nbsp;with a {rise}:{run} slope. &nbsp;Grid units are {units}.</p>\n<p><span data-jme-visible=\"debug\">d: {siground(d,3)} dperp: {siground(dperp,3) } theta: {siground(degrees(theta),3)}&nbsp;</span></p>\n<p></p>", "advice": "<ol>\n<li>Draw a diagram showing a triangle with sides that are the perpendicular distance $d_\\perp$ and direct distance $d = \\overline{AB}$.&nbsp;</li>\n<li>Use the distance formula to find the length of segment $\\overline{AB}$.</li>\n<li>Use trig to find the angle that segment $AB$ makes with the $x$- or $y$- axis.</li>\n<li>Use geometry to determine an angle in the triangle. &nbsp;Note that the angle that $d_\\perp$ makes with the vertical is the same as the angle that the line makes with the horizontal. &nbsp;Perpendicular lines have negative reciprocal slopes.</li>\n<li>Use trig with the known hypotenuse $d$&nbsp;and the angle to solve for perpendicular distance $d_\\perp$.</li>\n</ol>", "rulesets": {}, "extensions": ["geogebra", "quantities"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"dperp": {"name": "dperp", "group": "Ungrouped variables", "definition": "abs(cross(r,f))", "description": "<p>perpendicular distance from&nbsp;B to line</p>", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "Ungrouped variables", "definition": "arctan(Rise/Run)", "description": "<p>angle line makes with the horizontal</p>", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "abs(A-B)", "description": "<p>distance from A to B</p>", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "input", "definition": "vector(random(-6..6),random(-6..6))", "description": "<p>point on the line</p>", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "input", "definition": "A + vector(random(-5..5), random(-5..5))", "description": "<p>the point</p>", "templateType": "anything", "can_override": false}, "units": {"name": "units", "group": "Ungrouped variables", "definition": "random('in','ft','mm','cm','m')", "description": "", "templateType": "anything", "can_override": false}, "applet": {"name": "applet", "group": "input", "definition": "geogebra_applet('umrzknxw',params)", "description": "", "templateType": "anything", "can_override": false}, "params": {"name": "params", "group": "input", "definition": "[A: A, B: B, Rise: Rise, Run: Run, Z: Z]", "description": "", "templateType": "anything", "can_override": false}, "slopes": {"name": "slopes", "group": "input", "definition": "random([[1,2],[1,3],[1,5],[2,3],[3,4],[5,12]])", "description": "<p>pick a rise/run ratio for 'nice' choices</p>", "templateType": "anything", "can_override": false}, "slope": {"name": "slope", "group": "input", "definition": "random([[slopes[0],slopes[1]], [slopes[1],slopes[0]],[-slopes[0],slopes[1]], [-slopes[1],slopes[0]]])", "description": "<p>permutations of the legal slope</p>", "templateType": "anything", "can_override": false}, "Rise": {"name": "Rise", "group": "input", "definition": "slope[0]", "description": "<p>The rise</p>", "templateType": "anything", "can_override": false}, "Run": {"name": "Run", "group": "input", "definition": "slope[1]", "description": "<p>The run</p>", "templateType": "anything", "can_override": false}, "Z": {"name": "Z", "group": "input", "definition": "round(abs(A-B))+1", "description": "<p>Z sizes the ggb canvas to be large enough to show A and B</p>", "templateType": "anything", "can_override": false}, "r": {"name": "r", "group": "Ungrouped variables", "definition": "A-B + vector(0,0,0)\n", "description": "<p>3d vector from B to A</p>", "templateType": "anything", "can_override": false}, "F": {"name": "F", "group": "Ungrouped variables", "definition": "vector(cos(alpha),sin(alpha),0)", "description": "<p>3d unit vector &nbsp;for cross product to find angle theta and dperp</p>\n<p>(M= F d sin theta = r x F ), but |F|=1&nbsp;</p>", "templateType": "anything", "can_override": true}, "theta": {"name": "theta", "group": "Ungrouped variables", "definition": "degrees(angle(f,r))", "description": "<p>angle between line and segment d &nbsp;&nbsp;</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "0.2 < dperp/d < 0.8  and // not too close to 0 or 90\u00b0\nd > 3 // not too small", "maxRuns": 100}, "ungrouped_variables": ["d", "dperp", "debug", "units", "r", "alpha", "F", "theta"], "variable_groups": [{"name": "input", "variables": ["A", "B", "applet", "params", "slopes", "slope", "Rise", "Run", "Z"]}], "functions": {"applets": {"parameters": [], "type": "ggbapplet", "language": "javascript", "definition": "// Create the worksheet. \n// This function returns an object with a container `element` and a `promise` resolving to a GeoGebra applet.\nvar params = {\n  material_id: 'ptkds8nz'\n};\nvar result = Numbas.extensions.geogebra.createGeogebraApplet(params);\n\n// Once the applet has loaded, run some commands to manipulate the worksheet.\nresult.promise.then(function(d) {\n  var app = d.app;\n  question.applet = d;\n   \n  function setGGBPoint(name, nname=name) {\n    // moves point in GGB to Numbas value\n    var pt = Numbas.jme.unwrapValue(question.scope.getVariable(nname));\n    app.setFixed(name,false,false);\n    app.setCoords(name, pt[0], pt[1]);\n    app.setFixed(name,true,true);\n  }\n  \n   function setGGBAngle(gname, nname=gname) {\n    // Sets angle in GGB to a Numbas Variable given in degrees.\n    var v = Math.PI / 180 * Numbas.jme.unwrapValue(question.scope.getVariable(nname));\n    app.setValue(gname,v);\n  }  \n  \n  \n  setGGBPoint(\"A\");\n  setGGBPoint(\"B\");\n  setGGBAngle(\"\u03b1\",\"alpha\");\n  \n  \n});\n\n// This function returns the result of `createGeogebraApplet` as an object \n// with the JME data type 'ggbapplet', which can be substituted into the question's content.\nreturn new Numbas.jme.types.ggbapplet(result)"}, "show_triangle": {"parameters": [["app", "ggbapplet"], ["v", "boolean"]], "type": "anything", "language": "javascript", "definition": "// Take an applet, set its perspective to the given string.\n// See https://wiki.geogebra.org/en/SetPerspective_Command for the format of the perspective string.\napp.promise.then(function(d) {\n  d.app.setVisible(\"construction\", v);\n  d.app.setVisible(\"theta\", v);\n});\nreturn new Numbas.jme.types.ggbapplet(app);"}}, "preamble": {"js": "question.signals.on('adviceDisplayed',function() {\n  \n  try{\n    //var app = question.applet.app;\n    var app = Numbas.exam.currentQuestion.scope.variables.applet.app;\n    app.setVisible(\"construction\", true);\n    app.setVisible(\"theta\", true);  \n  }\n  catch(err){}  \n})\n\n", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Solutions", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find:</p>\n<p style=\"padding-left: 30px;\">The length of the segment $AB$:</p>\n<p style=\"padding-left: 60px;\">$d = $&nbsp;[[0]]</p>\n<p style=\"padding-left: 30px;\">The perpendicular distance between the point and the line:</p>\n<p style=\"padding-left: 60px;\">$d_{\\perp} = $ [[1]]&nbsp;</p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "d", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "quantity(abs(d), units)", "right": "0.1", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "dperp", "marks": "20", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "quantity(dperp, units)", "right": "0.1", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}]}], "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}