Combined Transformations

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Combined Transformations — Free MYP5 Mathematics (Standard) Practice Questions

1QuestionPerforming 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.

Determine the coordinates of the final image of

P

after both reflections. [1]

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

2QuestionDescribing 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

3QuestionDescribing 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.

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]

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

Solutions

4QuestionDescribing 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	$A_4(6,2)$	$B_4(8,2)$	$C_4(7,5)$

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

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

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

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