Identify the centre of enlargement and the scale factor in a transformation of an image A to an image B
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "advice": "You can find how image A has been enlarged to transform onto image B by drawing lines between the vertices of the image and extending them till they intersect.
\n{image('resources/question-resources/'+chosen_image[\"correct_image\"])}
\nThe centre of enlargement is the point where all the lines intersect. In this case, the centre of enlargement is $(\\var{answer_x},\\var{answer_y})$.
\nTo find the scale factor, identify a point on A and the corresponding point on B, and look at the coordinates of each relative to the centre of enlargement.
\nThe relative coordinates of the point on B are obtained by multiplying the relative coordinates of the point on A.
\nFrom the graph we can see the scale factor is $\\var{answer_scale}$.
", "statement": "Describe the transformation of image A to image B.
\n{image('resources/question-resources/'+chosen_image[\"image\"])}
", "preamble": {"js": "", "css": ""}, "variables": {"answer_y": {"name": "answer_y", "description": "", "templateType": "anything", "group": "Translation", "definition": "chosen_image[\"answer_y\"]"}, "correct_image": {"name": "correct_image", "description": "", "templateType": "anything", "group": "Translation", "definition": "chosen_image[\"correct_image\"]"}, "answer_scale": {"name": "answer_scale", "description": "", "templateType": "anything", "group": "Translation", "definition": "chosen_image[\"answer_scale\"]"}, "answer_x": {"name": "answer_x", "description": "", "templateType": "anything", "group": "Translation", "definition": "chosen_image[\"answer_x\"]"}, "enlargement_images": {"name": "enlargement_images", "description": "Is a list of the images in the images in the questions.
", "templateType": "anything", "group": "Translation", "definition": "['graph_enlargement_triangle_pos2_00.svg','graph_enlargement_triangle_neg2_00bJC2lDk.svg','graph_enlargement_rightangle_pos2_00.svg','graph_enlargement_rectangle_pos2_00.svg']"}, "chosen_image": {"name": "chosen_image", "description": "", "templateType": "anything", "group": "Translation", "definition": "random(images)"}, "images": {"name": "images", "description": "Uses JSON data to select the answer based on the image that is selected.
", "templateType": "json", "group": "Translation", "definition": "json_decode(safe(\"[\\n {\\n \\\"image\\\": \\\"graph_enlargement_triangle_pos2_00.svg\\\",\\n \\\"answer_x\\\": 0,\\n \\\"answer_y\\\": 0,\\n \\\"answer_scale\\\": 2,\\n \\\"correct_image\\\": \\\"graph_enlargement_triangle_pos2_00_correct_image.svg\\\"\\n },\\n {\\n \\\"image\\\": \\\"graph_enlargement_triangle_neg2_00_EoiLScE.svg\\\",\\n \\\"answer_x\\\": 0,\\n \\\"answer_y\\\": 0,\\n \\\"answer_scale\\\": -2,\\n \\\"correct_image\\\": \\\"graph_enlargement_triangle_neg2_00_correct_image_2mu3W4r.svg\\\"\\n },\\n {\\n \\\"image\\\": \\\"graph_enlargement_rightangle_pos2_00.svg\\\",\\n \\\"answer_x\\\": 0,\\n \\\"answer_y\\\": 0,\\n \\\"answer_scale\\\": 2,\\n \\\"correct_image\\\": \\\"graph_enlargement_rightangle_pos2_00_correct_image.svg\\\"\\n },\\n {\\n \\\"image\\\": \\\"graph_enlargement_rectangle_pos2_00.svg\\\",\\n \\\"answer_x\\\": 0,\\n \\\"answer_y\\\": 0,\\n \\\"answer_scale\\\": 2,\\n \\\"correct_image\\\": \\\"graph_enlargement_rectangle_pos2_00_correct_image.svg\\\"\\n }\\n]\"))"}}, "parts": [{"variableReplacementStrategy": "originalfirst", "prompt": "Centre of enlargement: ([[0]], [[1]])
", "gaps": [{"variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "maxValue": "{answer_x}", "allowFractions": false, "mustBeReducedPC": 0, "minValue": "{answer_x}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": 1, "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "maxValue": "{answer_y}", "allowFractions": false, "mustBeReducedPC": 0, "minValue": "{answer_y}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": 1, "scripts": {}}], "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "marks": 0, "showCorrectAnswer": true}, {"variableReplacementStrategy": "originalfirst", "prompt": "Scale factor: [[0]]
", "gaps": [{"variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "maxValue": "{answer_scale}", "allowFractions": false, "mustBeReducedPC": 0, "minValue": "{answer_scale}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": 1, "scripts": {}}], "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "marks": 0, "showCorrectAnswer": true}], "tags": ["centre of enlargement", "Centre of enlargement", "Enlargement", "enlargement", "Scale factor", "scale factor", "taxonomy", "transformation", "Transformation"], "variablesTest": {"maxRuns": 100, "condition": ""}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Aiden McCall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1592/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Aiden McCall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1592/"}]}