Transformations
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Transformations — Free MYP5 Mathematics (Extended) Practice Questions

1QuestionHorizontal shiftsConcept Practice
4 marks~6 minCriterion A
A drone follows a flight path modelled by f(x)=x2f(x) = x^2, where xx is horizontal distance (metres) and f(x)f(x) is height (metres). An adjusted path is modelled by g(x)=(x−3)2g(x) = (x-3)^2.
a
Deduce the coordinates of the vertex of gg. [1]
b
Calculate g(7)g(7) and explain what this value represents in the context of the drone's flight path. [2]
c
The drone must reach a height of at least 10 metres by the time it has travelled 6 metres horizontally. Advise the drone operator whether the adjusted path gg satisfies this requirement, justifying your answer with a calculation. [1]
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2QuestionCombined transformationsAssessment Practice
2 marks~3 minCriterion D
A graphic designer uses a triangle with vertices at A(1,2)A(1, 2), B(3,2)B(3, 2), and C(2,5)C(2, 5). She first translates the triangle by the vector (4−1)\begin{pmatrix} 4 \\ -1 \end{pmatrix}, then reflects the resulting triangle across the vertical line x=6x = 6.

Justify whether this mathematical model is reliable for a designer working with a physical stencil on a printed page. [2]
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3QuestionReflectionsConcept Practice
2 marks~3 minCriterion B
A graphic designer uses coordinate geometry to create a reflected logo. The original logo contains the point P(3,−5)P(3, -5). The designer reflects the entire logo across the xx-axis, as shown by the pattern below.

(2, 3)→(2, −3)(2,\ 3) \rightarrow (2,\ -3)

(−1, 5)→(−1, −5)(-1,\ 5) \rightarrow (-1,\ -5)

(4, −2)→(4, 2)(4,\ -2) \rightarrow (4,\ 2)

Deduce the general rule for reflecting any point (x,y)(x, y) across the xx-axis. [1]

State the image of P(3,−5)P(3, -5) after reflection across the xx-axis. [1]

Solutions

4QuestionStretch/compressionAssessment Practice
6 marks~9 minCriterion C
A graphic designer is resizing a logo for a billboard and a business card. The logo's outline is defined by vertices A(2, 1)A(2,\ 1), B(6, 1)B(6,\ 1), C(7, 4)C(7,\ 4), and D(1, 4)D(1,\ 4). The designer applies a vertical stretch by factor 2.52.5, followed by a horizontal compression by factor 0.40.4.
a
Determine the coordinates of the transformed vertices A′A', B′B', C′C', and D′D' after both transformations are applied in the given order. [2]
b
Calculate the area of the original logo and the area of the transformed logo. Show that the two areas are equal, and explain why this result occurs. [2]
c
Advise the designer whether this transformation is suitable for both media, justifying your answer with reference to the effect of non-uniform scaling on the logo's proportions and the significance of the equal-area result. [2]
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