Geometrical Transformations

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Geometrical Transformations — Free MYP5 Mathematics (Standard) Practice Questions

1QuestionDescribing and Performing TranslationsConcept Practice

4 marks~6 minCriterion A

A city planner uses a coordinate grid to map a triangular green space with vertices at

A(1, 2)

B(3, 5)

, and

C(4, 1)

. The entire triangle is translated so that

A

maps to

A'(5, 3)

Calculate the translation vector that maps triangle

ABC

to triangle

A'B'C'

. Give your answer in the form

\begin{pmatrix} x \\ y \end{pmatrix}

. [1]

Determine the coordinates of

B'

and

C'

. [1]

A second translation,

\begin{pmatrix} -2 \\ 4 \end{pmatrix}

, is then applied to the whole triangle. The planner claims that vertex

A

now lies within the region

x > 2

and

y > 6

. Justify whether this claim is correct. [2]

Solutions

2QuestionEnlargement with Positive and Negative Scale FactorsAssessment Practice

4 marks~6 minCriterion D

An architect designs a building with a rectangular footprint. The corners on the blueprint are:

A(2,\ 1),\quad B(6,\ 1),\quad C(6,\ 4),\quad D(2,\ 4)

A scale model is produced by applying an enlargement with scale factor

k = 0.02

, centred at the origin. A mirror-image wing is then modelled by applying an enlargement with scale factor

k = -1

, centred at the origin, to the original coordinates.

Calculate the coordinates of

A'

B'

C'

D'

after the enlargement

k = 0.02

. [1]

Calculate the coordinates of

A''

B''

C''

D''

after the enlargement

k = -1

. [1]

Advise the architect whether the mirror-image wing produced by

k = -1

can be directly used as a construction plan, referring to at least two real-world constraints in your response. [2]

Solutions

3QuestionReflections in Lines x-axis y-axis y=x y=-xAssessment Practice

4 marks~6 minCriterion B

A graphic designer is creating a logo using reflected line segments on a coordinate grid. The segment

MN

has endpoints

M(-4,\, 2)

and

N(-1,\, 5)

. The designer reflects

MN

across the line

y = x

to produce image segment

M'N'

Calculate the gradient of segment

MN

. [1]

Deduce the coordinates of

M'

and

N'

, and hence calculate the gradient of segment

M'N'

. [1]

The designer claims that any line segment parallel to

y = x

is unaffected by reflection in

y = x

. Analyse the gradients of

MN

and

M'N'

to justify whether this claim is mathematically valid, with reference to the general effect of this reflection on gradients. [2]

Solutions

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

4 marks~6 minCriterion C

A graphic designer is creating a logo by reflecting a triangular motif. Triangle

ABC

has vertices

A(1, 2)

B(3, 5)

, and

C(4, 1)

. The triangle is reflected in the

x

-axis to produce image triangle

A'B'C'

State the coordinates of

B'

. [1]

Determine the coordinates of

A'

and

C'

. [1]

The designer claims the reflected motif is identical to the original and can replace it in any orientation. Justify whether this claim is correct, using the coordinates of the triangle and its image. [2]

Solutions

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