Transformations — Free IB MYP5 Mathematics (Standard) 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)

.

a

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]

b

Determine the coordinates of

B'

and

C'

. [1]

c

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

2QuestionPerforming Two Successive TransformationsConcept Practice

2 marks~3 minCriterion A

A graphic designer uses a coordinate grid to position a logo element. The anchor point of the element is at

P(3, 4)

.

The designer first reflects

P

across the

x

-axis, then reflects the resulting point across the

y

-axis.

a

Determine the coordinates of the final image of

P

after both reflections. [1]

b

The designer needs the final anchor point to lie in the third quadrant to align with the page layout. Justify whether the two reflections meet this requirement. [1]

Solutions

3QuestionEnlargement 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.

a

Calculate the coordinates of

A'

,

B'

,

C'

,

D'

after the enlargement

k = 0.02

. [1]

b

Calculate the coordinates of

A''

,

B''

,

C''

,

D''

after the enlargement

k = -1

. [1]

c

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

4QuestionReflections 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'

.

a

Calculate the gradient of segment

MN

. [1]

b

Deduce the coordinates of

M'

and

N'

, and hence calculate the gradient of segment

M'N'

. [1]

c

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

5QuestionReflections 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'

.

a

State the coordinates of

B'

. [1]

b

Determine the coordinates of

A'

and

C'

. [1]

c

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

6QuestionDescribing Combined Transformations in Real-Life ContextsAssessment Practice

6 marks~9 minCriterion B

A graphic designer uses a repeating tile pattern. A triangle with vertices

A(0,0)

,

B(2,0)

,

C(1,3)

is transformed repeatedly to produce a sequence of images.

Image 1	$A_1(0,0)$	$B_1(2,0)$	$C_1(1,3)$
Image 2	$A_2(2,2)$	$B_2(4,2)$	$C_2(3,5)$
Image 3	$A_3(4,0)$	$B_3(6,0)$	$C_3(5,3)$
Image 4	$A_4(6,2)$	$B_4(8,2)$	$C_4(7,5)$

a

Construct Image 5 and Image 6 on the coordinate grid provided. Describe the pattern you observe in the sequence. [2]

b

Deduce the general rule for the transformation that maps each image to the next, expressing it as a combination of translations. [2]

c

The designer considers extending the tile pattern using a new triangle with vertices

D(0,0)

,

E(3,0)

,

F(1,2)

. Apply your rule to find the vertices after one transformation, then justify whether this new triangle would produce a valid repeating tile pattern consistent with the original sequence. [2]

Solutions

7QuestionDescribing Combined Transformations in Real-Life ContextsAssessment Practice

2 marks~3 minCriterion C

A graphic designer maps a logo element using triangle

ABC

with vertices

A(1, 2)

,

B(4, 2)

, and

C(4, 6)

. The triangle is reflected in the

y

-axis and then translated by the vector

\begin{pmatrix} 3 \\ -5 \end{pmatrix}

to produce triangle

A'B'C'

.

Identify one geometric property that is preserved under this combined transformation, and justify why both rigid transformations guarantee this property is unchanged. [2]

Solutions

8QuestionDescribing Combined Transformations in Real-Life ContextsAssessment Practice

2 marks~3 minCriterion D

A graphic designer applies a translation of

5 \text{ cm}

to the right to a triangular logo element, then reflects it across a vertical line of symmetry to produce a mirrored pattern.

a

Describe one real-world context, other than logo design, in which a translation followed by a reflection is used to create a symmetrical pattern. [1]

b

The designer measures the translation distance imprecisely. Explain how this error affects the symmetry of the final pattern. [1]

Solutions

Transformations — Free MYP5 Mathematics (Standard) Practice Questions