// Numbas version: exam_results_page_options {"name": "Numbastest uke 34: Plangeometri", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], []], "questions": [{"name": "Rett linje", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mario Orsi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/427/"}, {"name": "Mark Hodds", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/510/"}, {"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "

Students are supposed to use Excel (or similar) to find the answers (e.g., enter coordinates of two points then plot and add trendline).

Uses an embedded Geogebra graph of a line $y=mx+c$ with random coefficients set by NUMBAS.

", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "

{geogebra_applet('https://www.geogebra.org/m/rsb3yw2a', defs, [])}

Se på den rette linjen ovenfor og svar følgende spørsmål:

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Bruk formelen for stigningstallet $m=\\frac{y_2-y_1}{x_2-x_1}$

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Hva er stigningstallet?

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Hva er konstantleddet?

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Linkningen til linja blir da

$y=$[[0]]

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Finn $y$ for $x=\\var{x1}$

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Finn $x$ når $y=\\var{y2}$

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Uttrykkene representerer rette linjer. For hvert uttrykk i den loddrette listen skal dere velge hvilket av alternativene i den vannrette listen som gir en parallell linje.

", "advice": "

To rette linjer med samme stigningstall kalles parallelle.

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Uttrykkene representerer rette linjer. For hvert uttrykk i den loddrette listen skal dere velge uttrykket for en linje som står vinkelrett på denne.

", "advice": "

To rette linjer $y=a_1x+b_1$ og $y=a_2x+b_2$ sies å stå vinkelrett (eller normalt) på hverandre hvis stigningstallene oppfyller $a_2=-\\dfrac{1}{a_1}$

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{geogebra_applet('https://www.geogebra.org/m/uxnywnms',defs)}

Der er gitt to punkter ovenfor

", "advice": "

Med avstanden mellom punktene $(x_1,y_1)$ og $(x_2,y_2)$ i planet menes

$d=\\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.

Lengden av et linjestykke er avstanden mellom dets endepunkter.

Finn avstanden mellom punktene $A$ og $B$. Angi svaret ved bruk av kvadratrot (bruk sqrt(tall) for å skrive $\\sqrt{tall}$).

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{geogebra_applet('https://www.geogebra.org/m/qt6cja4h',defs)}

Beskriv området over som et produkt av to intervaller

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$[$[[0]],[[1]]$]\\times[$[[2]],[[3]]$]$

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For hvert område finn passende beskrivelse

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