// Numbas version: exam_results_page_options
{"name": "Distanza e punto medio tra due punti nel piano cartesiano", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Distanza e punto medio tra due punti nel piano cartesiano", "tags": [], "metadata": {"description": "<p style=\"-webkit-user-select: auto;\">Esercizio che chiede di calcolare la distanza e il punto medio tra due punti di coordinate intere assegnate. La distanza \u00e8 sempre un numero naturale.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Dati i punti $A ( \\var{x_A} ; \\var{y_A} )$ e $B ( \\var{x_B} ; \\var{y_B} )$, determina:</p>", "advice": "<p style=\"text-align: justify;\"><strong>a)</strong> Il segmento $AB$ &egrave; l'ipotenusa del triangolo rettangolo di cateti $| x_B - x_A | = | \\simplify[!collectNumbers]{{x_B} - {x_A}} | = \\var{abs(x_B-x_A)}$ e $| y_B - y_A | = |\\simplify[!collectNumbers]{{y_B} - {y_A}}| = \\var{abs(y_B - y_A)}$; usando il teorema di Pitagora otteniamo $A B = \\sqrt{{(x_B - x_A)}^2 + {(y_B - y_A)}^2} = \\sqrt{\\simplify[!collectNumbers]{{({x_B-x_A})}^2 + {({y_B-y_A})}^2}} = \\sqrt{\\var{(x_B-x_A)^2+(y_B-y_A)^2}} =&nbsp;\\var{sqrt((x_B-x_A)^2+(y_B-y_A)^2)}$.</p>\n<p style=\"text-align: justify;\"><strong>b)</strong> Le coordinate del punto $M$ sono la media tra le coordinate di $A$ e $B$: $x_M = \\frac{x_A + x_B}{2} = \\frac{\\simplify[!collectNumbers]{{x_A}+({x_B})}}{2} = \\var[fractionNumbers]{(x_A+x_B)/2}$, $y_M = \\frac{y_A + y_B}{2}&nbsp;= \\frac{\\simplify[!collectNumbers]{{y_A}+({y_B})}}{2} = \\var[fractionNumbers]{(y_A+y_B)/2}$.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"x_A": {"name": "x_A", "group": "Ungrouped variables", "definition": "random(-8 .. 8#1)", "description": "<p>Ascissa del punto $A$: un numero intero tra $- 6$ e $6$.</p>", "templateType": "randrange", "can_override": false}, "y_A": {"name": "y_A", "group": "Ungrouped variables", "definition": "y_B+2*k*m*n", "description": "<p>Ordinata&nbsp;del punto $A$: in modo che $A$ e $B$ abbiano una distanza intera (coordinate di $B - A$ in terna pitagorica con la distanza)</p>", "templateType": "anything", "can_override": false}, "x_B": {"name": "x_B", "group": "Ungrouped variables", "definition": "x_A+k*(m^2-n^2)", "description": "<p>Ascissa del punto $B$: in modo che $A$ e $B$ abbiano una distanza intera (coordinate di $B - A$ in terna pitagorica con la distanza)</p>", "templateType": "anything", "can_override": false}, "y_B": {"name": "y_B", "group": "Ungrouped variables", "definition": "random(-8 .. 8#1)", "description": "<p>Ordinata del punto $B$: un numero intero tra $- 10$ e $10$.</p>", "templateType": "randrange", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(-4..4 except 0)", "description": "<p>Primo generatore&nbsp;di una terna pitagorica</p>", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(-4..4 except [-m,0,m])", "description": "<p>Secondo generatore di una terna pitagorica</p>", "templateType": "anything", "can_override": false}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "1", "description": "<p>Costante moltiplicativa della terna pitagorica</p>", "templateType": "number", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x_A", "y_A", "x_B", "y_B", "m", "n", "k"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "a)", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>la distanza tra i punti $A$ e $B$: &nbsp;&nbsp;[[0]]</p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "distanza", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "sqrt(({x_B-x_A})^2+(y_B-y_A)^2)", "maxValue": "sqrt(({x_B-x_A})^2+(y_B-y_A)^2)", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": "90", "displayAnswer": "", "showFractionHint": false, "notationStyles": ["plain", "si-en", "si-fr", "plain-eu"], "correctAnswerStyle": "plain-eu"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "b)", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>le coordinate del punto medio $M$ del segmento $A B$: &nbsp; $M$([[0]];&nbsp;[[1]])</p>\n<p>(Per la linea di frazione usa il carattere \"/\".)</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "x_M", "marks": ".5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "(x_A+x_B)/2", "maxValue": "(x_A+x_B)/2", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": "90", "displayAnswer": "", "showFractionHint": false, "notationStyles": ["plain", "si-en", "si-fr", "plain-eu"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "y_M", "marks": ".5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "(y_A+y_B)/2", "maxValue": "(y_A+y_B)/2", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": "90", "displayAnswer": "", "showFractionHint": false, "notationStyles": ["plain", "si-en", "si-fr", "plain-eu"], "correctAnswerStyle": "plain-eu"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Irene Paniccia", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4869/"}]}]}], "contributors": [{"name": "Irene Paniccia", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4869/"}]}