Combined Transformations 2

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Combined Transformations 2 — Free MYP4 Mathematics (Extended) Practice Questions

1QuestionDescribing Combined Transformations in Real-Life ContextsConcept Practice

3 marks~5 minCriterion A

A logo designer places a triangle on a coordinate grid with vertices at

A(1, 3)

B(4, 1)

, and

C(2, -2)

. The designer first translates the triangle by the vector

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

, then reflects the result over the

y

-axis.

Calculate the coordinates of

A'

B'

, and

C'

after the translation. [1]

Calculate the final coordinates of

A''

B''

, and

C''

after the reflection. [1]

The designer requires the final logo to sit entirely in the third quadrant. Justify whether this condition is met. [1]

Solutions

2QuestionPerforming Two Successive TransformationsAssessment Practice

2 marks~3 minCriterion D

A graphic designer places a triangular logo on a coordinate grid. The logo is first translated 3 units right and 2 units upward to centre it on the billboard layout, then reflected across the

y

-axis to produce a mirrored version for the opposite side of the billboard.

Critique the use of this coordinate grid method for positioning the logo on an actual billboard.

[2]

Solutions

3QuestionIdentifying and Describing Single TransformationsAssessment Practice

4 marks~6 minCriterion C

An architect designs a symmetrical building wing. The original section is a right-angled triangle with vertices at

A(2, 1)

B(5, 1)

, and

C(5, 4)

on a coordinate grid (units in metres). The wing is reflected across the vertical line

x = 6

to create a mirror-image section.

Describe the single transformation that maps triangle

ABC

to its image

A'B'C'

, stating the coordinates of

A'

B'

, and

C'

. [2]

A construction error causes the intended reflection axis

x = 6

to be rotated

3°

clockwise about the point

(6, 0)

. Explain how this error affects the position of the reflected section, and why the displacement is not the same for all three vertices. [1]

The architect claims the reflected design will remain a perfect mirror image of the original wing throughout the building's lifetime. Assess the validity of this claim, considering how real structures behave over time. [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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