Geometrical Transformations

You're viewing free preview questions — 4 questions previewing here — subscribe to unlock 94 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

Geometrical Transformations — Free MYP4 Mathematics (Standard) Practice 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 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)

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

A

B

in column vector form. [1]

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]

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

3QuestionReflections 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)

Identify the line of reflection. [1]

Deduce the general transformation rule

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

for a reflection across this line. [1]

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

4QuestionDescribing 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)

Determine the translation vector that maps

A

B

. [1]

A fountain is located at

C(-3, 4)

. Deduce the coordinates of its image

C'

after applying the same translation. [1]

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

Questions 5-98

Unlock these questions with Premium

That's every free question here — 4 of 98.

+94 more questions, plus Mock Papers & Worksheets, are waiting in Premium.

Upgrade