Transformations — Free IB MYP4 Mathematics (Standard) Questions

1QuestionRotations About a Point and AngleConcept Practice

2 marks~3 minCriterion A

A security camera mounted at the origin of a coordinate grid rotates to track a moving object. The camera first points toward

A(3,\ 2)

, then rotates to point toward

A'(-2,\ 3)

.

State the angle and direction of this rotation about the origin, and write the general coordinate rule that describes it. [2]

Solutions

2QuestionDescribing 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.

a

Calculate the coordinates of

A'

, the image of

A

after the translation. [1]

b

Deduce the coordinates of

A''

, the final image of

A

after both transformations. [1]

c

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

3QuestionDescribing and Performing TranslationsAssessment Practice

4 marks~6 minCriterion C

A map grid uses coordinates measured in kilometres. A cargo ship travels from port

A(-4,\ 3)

to port

B(5,\ -2)

.

a

Write the translation vector that describes the ship's journey from

A

to

B

in column vector form. [1]

b

A second cargo ship starts at port

C(-1,\ -3)

and follows the same translation vector. Determine the coordinates of its final position,

C'

. [1]

c

The harbour authority rescales the map so that each grid unit now represents 2 km instead of 1 km. The second ship's captain claims the translation vector must change because the real-world distances have doubled. Justify whether the captain's claim is correct, referring to the components of the vector and what they represent on each map. [2]

Solutions

4QuestionReflections in Lines x-axis y-axis y=x y=-xAssessment Practice

4 marks~6 minCriterion D

A graphic designer is creating a symmetrical logo. Point

P(-3, 4)

represents a vertex of the logo, and its mirror image is at

P'(3, 4)

.

a

Identify the line of reflection. [1]

b

Deduce the general transformation rule

(x, y) \to (\ ?\ ,\ ?\ )

for a reflection across this line. [1]

c

The designer claims that

P

and

P'

are positioned symmetrically about the line of reflection, so the logo will appear balanced. Justify this claim by calculating the perpendicular distance from each point to the line of reflection and explaining what your result means for the logo design. [2]

Solutions

5QuestionDescribing and Performing TranslationsAssessment Practice

4 marks~6 minCriterion B

A city planner uses a coordinate grid to map pedestrian pathways. A translation arrow on the grid shows that gateway

A(1, 2)

maps to gateway

B(6, -3)

.

a

Determine the translation vector that maps

A

to

B

. [1]

b

A fountain is located at

C(-3, 4)

. Deduce the coordinates of its image

C'

after applying the same translation. [1]

c

The planner considers two successive pathway shifts: the translation from part (a) and a second translation

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

. Advise the planner whether the order in which the two shifts are applied affects the final mapped position of the fountain, justifying your answer with calculations. [2]

Solutions

6QuestionFinding 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

.

a

Determine the coordinates of the image of

P

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

b

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]

c

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

7QuestionIdentifying 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.

a

Describe the single transformation that maps triangle

ABC

to its image

A'B'C'

, stating the coordinates of

A'

,

B'

, and

C'

. [2]

b

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]

c

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

8QuestionIdentifying 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}

.

a

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

b

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]

c

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

Solutions

Transformations — Free MYP4 Mathematics (Standard) Practice Questions