Enlargement and Scale Factor
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Enlargement and Scale Factor — Free MYP3 Mathematics Practice Questions

1QuestionComparing Original and Enlarged ShapesConcept Practice
2 marks~3 minCriterion A
Triangle ABCABC has vertices at A(1,1)A(1,1), B(3,1)B(3,1), and C(2,4)C(2,4). It is enlarged by a scale factor of 2 about the origin to produce triangle A′B′C′A'B'C', with vertices at A′(2,2)A'(2,2), B′(6,2)B'(6,2), and C′(4,8)C'(4,8).
a
Identify the vertex in triangle A′B′C′A'B'C' that corresponds to vertex BB. [1]
b
Explain which side of triangle A′B′C′A'B'C' corresponds to side BCBC, and why. [1]
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Solutions

2QuestionDrawing Enlarged Shapes Using Grid MethodsAssessment Practice
5 marks~8 minCriterion B
Triangle ABCABC has vertices at A(2,1)A(2, 1), B(6,1)B(6, 1), and C(6,5)C(6, 5). It is enlarged with centre of enlargement (2,1)(2, 1) and scale factor 0.50.5.

A student claims: "The enlarged image has one-quarter the area of the original triangle."
a
Calculate the coordinates of the vertices of the enlarged triangle A′B′C′A'B'C'. [1]
b
Calculate the area of triangle ABCABC and the area of triangle A′B′C′A'B'C'. Show all working. [2]
c
Justify whether the student's claim is correct, referring to the relationship between scale factor and area. [2]
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Solutions

3QuestionComparing Original and Enlarged ShapesAssessment Practice
6 marks~9 minCriterion D
A cartographer enlarges a master map using a scale factor of 2.5 to produce a wall map. The master map has a printing tolerance of ±0.3 cm per measurement. The distance between two cities on the master map is recorded as 12.0 cm.
a
Calculate the maximum possible error in the enlarged distance on the wall map. [2]
b
Explain how this error affects the usefulness of the wall map for navigation. [2]
c
Analyse why using a single scale factor to enlarge a map with measurement tolerances limits the map's reliability for precise navigation. [2]
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Solutions

4QuestionComparing Original and Enlarged ShapesAssessment Practice
6 marks~9 minCriterion C
A student uses a photocopier to enlarge a rectangular photo. The original photo measures 5 cm by 8 cm. The photocopier is set to 150% enlargement. The printed copy measures 7.4 cm by 12.1 cm.
a
Calculate the scale factor for each dimension using the printed measurements. Express each answer as a decimal. [2]
b
The expected scale factor for a 150% enlargement is 1.5. Compare your scale factors from part (a) to this expected value and explain whether the photocopier produced an accurate enlargement. [2]
c
A student suggests that measuring just one dimension of the printed copy is enough to check the photocopier's accuracy. Analyse this suggestion, identifying two reasons why a single measurement may not be reliable. [2]
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Solutions

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