SkillrHub • Year 7 Maths

AC9M7SP03 • Homework

Transformations in the Cartesian Plane

Describe translations, reflections and rotations precisely. Show intermediate coordinates for multi-step transformations and check which geometric properties are preserved.

5 × 2 marks
Short response
5 × 5 marks
Extended reasoning
1 enrichment
Pattern sequence

Part A — Short response

  1. Describe the translation mapping (3,−2) to (8,4). (2)
  2. Reflect (−4,7) in the x-axis. (2)
  3. Rotate (2,5) 180° about the origin. (2)
  4. What transformation is represented by (x,y)→(x,−y)? (2)
  5. A point moves from (1,3) to (1,−3). Identify the transformation. (2)

Part B — Extended response

  1. Triangle A(1,2), B(4,2), C(4,6) is translated by (x,y)→(x+3,y−1). List A', B', C' and describe what is preserved. (5)
  2. Reflect P(2,3), Q(5,3), R(5,7) in the y-axis. Give all image coordinates and explain the change in orientation. (5)
  3. Rotate (3,−4) 90° anticlockwise about the origin, then reflect the result in the x-axis. Show both stages. (5)
  4. Use point (2,3) to demonstrate that reflection in x=1 followed by reflection in x=5 is equivalent to a translation. State the net translation. (5)
  5. Rotate (6,−1) 180° about the origin and then translate by (−3,+2). Find the final coordinate and describe the sequence precisely. (5)

Part C — Enrichment

11. Pattern transformation sequence. Start with A(2,1). Apply, in order: (1) reflection in the y-axis, (2) translation (+4,+3), (3) rotation 90° anticlockwise about the origin, (4) reflection in the x-axis. Record every intermediate coordinate, give the final coordinate, and explain how repeating transformation sequences can create precise digital geometric patterns.

Answers

1

(+5,+6): 5 right and 6 up.

2

(−4,−7).

3

(−2,−5).

4

Reflection in the x-axis.

5

Reflection in the x-axis.

6

A'=(4,1), B'=(7,1), C'=(7,5). Lengths, angles, size, shape and orientation are preserved.

7

P'=(−2,3), Q'=(−5,3), R'=(−5,7). Size and shape are preserved; orientation is reversed.

8

(3,−4)→(4,3)→(4,−3).

9

(2,3)→(0,3)→(10,3). Net translation (+8,0), twice the 4-unit separation of the parallel mirror lines.

10

(6,−1)→(−6,1)→(−9,3).

11

(2,1)→(−2,1)→(2,4)→(−4,2)→(−4,−2). Repeating controlled flips, slides and turns can generate congruent repeated motifs, symmetric designs and transformation patterns.