Translating Reflecting Rotating Shapes

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Translating Reflecting Rotating Shapes — Free MYP3 Mathematics Practice Questions

1QuestionCombining Multiple TransformationsConcept Practice

2 marks~3 minCriterion A

Triangle

ABC

has vertices at

A(1, 2)

B(3, 2)

, and

C(2, 5)

.

The triangle is first reflected in the

y

-axis, then translated 2 units to the left.

Apply the reflection in the

y

-axis to find the image of point

C

. [1]

Apply the translation to your answer from part (a) to find the final image of point

C

. [1]

Solutions

2QuestionRotating Shapes Around the OriginAssessment Practice

6 marks~9 minCriterion B

Points

A(1,0)

B(0,1)

C(-1,0)

, and

D(0,-1)

are plotted on the coordinate grid provided.

Apply a 90° counterclockwise rotation about the origin to each point. Record the new coordinates and describe the pattern you observe. [2]

Explain how the pattern from part (a) predicts the image of

(3,-2)

after a 90° counterclockwise rotation, then calculate the image coordinates. [2]

A student claims that a 270° counterclockwise rotation about the origin maps

(3,-2)

(-2,-3)

. Analyse whether this claim is correct by applying the rotation rule twice from part (a) and justifying your conclusion. [2]

Solutions

3QuestionTranslating Shapes on a GridConcept Practice

5 marks~8 minCriterion C

Triangle

ABC

has vertices

A(-2, 1)

B(0, 4)

, and

C(3, -1)

. A student translates the triangle by the vector

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

and claims the image vertices are

A'(-5, 3)

B'(-3, 6)

, and

C'(0, 1)

Calculate the coordinates of

A'

B'

, and

C'

after the translation. [3]

Compare your calculated coordinates with the student's claimed image points and state whether the claim is correct. [1]

A second student translates only vertex

C(3, -1)

and records the image as

C'(0, -3)

. Explain what mistake this student likely made. [1]

Solutions

4QuestionDescribing Transformations in WordsAssessment Practice

6 marks~9 minCriterion D

A city planner uses a coordinate grid to model a building's noon shadow. The building is triangle

ABC

with vertices

A(2, 1)

B(2, 5)

, and

C(5, 1)

. The model assumes the building is perfectly vertical, so the shadow is a reflection of triangle

ABC

across the x-axis.

Apply the reflection rule

(x, y) \rightarrow (x, -y)

to find the coordinates of

A'

B'

, and

C'

. [2]

Explain why a reflection across the x-axis correctly models the shadow of a perfectly vertical building. [2]

The building actually leans slightly to the right. Describe a transformation that would better model the real shadow, and explain why the reflection model is no longer sufficient. [2]

Solutions

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