Combining Transformations
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Combining Transformations — Free MYP3 Mathematics Practice Questions

1QuestionApplying Two or More Transformations SequentiallyConcept Practice
2 marks~3 minCriterion A
A triangle has vertices at A(1,2)A(1, 2), B(3,2)B(3, 2), and C(2,5)C(2, 5).

The triangle is first reflected across the yy-axis, then translated 3 units to the right.

Calculate the coordinates of vertex C(2,5)C(2, 5) after both transformations. [2]
Question diagram

Solutions

2QuestionIdentifying Final Image After Multiple TransformationsAssessment Practice
6 marks~9 minCriterion D
A drone delivery service uses a coordinate grid to plan its flight path. The drone starts at point A(2,3)A(2, 3). It translates by the vector (4−2)\begin{pmatrix}4\\-2\end{pmatrix} to reach point BB, then reflects over the line y=−1y = -1 to reach the drop zone at point CC.
a
Calculate the coordinates of point BB. [2]
b
Calculate the coordinates of point CC after the reflection over y=−1y = -1. [2]
c
Analyse one way in which using a 2D coordinate grid to model the drone's flight path may not reflect real-world conditions. Use the context to support your answer. [2]
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Solutions

3QuestionApplying Two or More Transformations SequentiallyAssessment Practice
7 marks~11 minCriterion C
A graphic designer places a logo at point P(2, 1)P(2,\ 1) on a coordinate grid. She applies a translation of (4, −3)(4,\ -3) followed by a 90°90° clockwise rotation about the origin. Her colleague claims the final position would be the same if the rotation were applied first.
a
Apply the translation (4, −3)(4,\ -3) then the 90°90° clockwise rotation to P(2, 1)P(2,\ 1). State the final coordinates. [2]
b
Apply the 90°90° clockwise rotation then the translation (4, −3)(4,\ -3) to P(2, 1)P(2,\ 1). State the final coordinates. [2]
c
Compare your results from parts (a) and (b) and analyse whether the colleague's claim is valid. In your answer, explain why the order of transformations matters and describe one consequence of assuming transformations can always be reordered. [3]
Question diagram

Solutions

4QuestionApplying Two or More Transformations SequentiallyAssessment Practice
6 marks~9 minCriterion B
A point (x,y)(x, y) is transformed by the following sequence: reflect in the yy-axis, then translate by the vector (4−1)\begin{pmatrix}4\\-1\end{pmatrix}, then reflect in the xx-axis.
a
Apply this transformation sequence to each point below and record the final coordinates. [2]

A(2, 3)A(2,\ 3) \quad B(−1, 5)B(-1,\ 5) \quad C(0, −4)C(0,\ -4) \quad D(3, −2)D(3,\ -2)
b
Using your results from part (a), explain how you can write a single rule (x′,y′)=(…, …)(x', y') = (\ldots,\ \ldots) that gives the final coordinates directly from (x,y)(x, y). State your rule. [2]
c
A student claims the rule gives the same result as applying the three steps one at a time. Choose a point not used in part (a), apply both methods, and justify whether the student's claim is correct. [2]

Solutions

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