Combined Transformations

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Combined Transformations — Free MYP4 Mathematics (Standard) Practice Questions

1QuestionDescribing Combined Transformations in Real-Life ContextsConcept Practice

4 marks~6 minCriterion A

A graphic designer is mapping a logo onto a coordinate grid. The logo contains a triangle with vertices at

A(1, 2)

B(4, 2)

, and

C(3, 5)

. The triangle is first translated by the vector

\begin{pmatrix} -3 \\ 4 \end{pmatrix}

, then reflected in the

x

-axis to produce the final image.

Calculate the coordinates of

A'

, the image of

A

after the translation. [1]

Deduce the coordinates of

A''

, the final image of

A

after both transformations. [1]

The designer claims the final image of the triangle lies entirely below the

x

-axis. Justify whether this claim is correct by applying both transformations to vertices

B

and

C

. [2]

Solutions

2QuestionIdentifying and Describing Single TransformationsAssessment Practice

4 marks~6 minCriterion D

An architect designs a symmetrical building wing. The original section is a right-angled triangle with vertices at

A(2, 1)

B(5, 1)

, and

C(5, 4)

on a coordinate grid (units in metres). The wing is reflected across the vertical line

x = 6

to create a mirror-image section.

Describe the single transformation that maps triangle

ABC

to its image

A'B'C'

, stating the coordinates of

A'

B'

, and

C'

. [2]

A construction error causes the intended reflection axis

x = 6

to be rotated

3°

clockwise about the point

(6, 0)

. Explain how this error affects the position of the reflected section, and why the displacement is not the same for all three vertices. [1]

The architect claims the reflected design will remain a perfect mirror image of the original wing throughout the building's lifetime. Assess the validity of this claim, considering how real structures behave over time. [1]

Solutions

3QuestionFinding the Single Equivalent TransformationAssessment Practice

6 marks~9 minCriterion B

A graphic designer places a logo element at point

P(2, 3)

on a coordinate grid. To reposition it, the designer applies two successive reflections: first across the line

y = x

, then across the line

y = -x

Determine the coordinates of the image of

P

after both reflections are applied in order. Show your working. [2]

Deduce the single rotation about the origin that produces the same final image as the two reflections combined. State the angle and justify why direction need not be specified. [2]

The designer claims this rotation model can guide the physical placement of a logo using two angled mirrors. Assess whether the model is reliable for a real printing process, identifying the key factors that could cause the actual logo position to differ from the predicted position. [2]

Solutions

4QuestionIdentifying and Describing Single TransformationsAssessment Practice

6 marks~9 minCriterion C

A graphic designer is creating a logo. A triangular element has vertices

A(2,3)

B(4,5)

C(6,3)

. After transformation, the image has vertices

A'(5,1)

B'(7,3)

C'(9,1)

. The designer claims the transformation is a translation by vector

\begin{pmatrix} 3 \\ -2 \end{pmatrix}

Determine the displacement vector mapping each vertex to its image. Justify whether the designer's claim is correct. [3]

The original coordinates carry a measurement error of

\pm 1

unit. Explain how such an error could cause the transformation to be misidentified as a reflection or rotation rather than a translation. [2]

Advise the designer whether coordinate geometry alone is sufficient for describing transformations in hand-drawn logo sketches. [1]

Solutions

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