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Transformations Practice Problems with Solutions - IGCSE Year 9

IGCSE Year 9 | Math | Transformations
Name: _________________________ Date: _________________________ Score: _______ / 40

Reflecting (3, 4) in the y-axis maps it to (−3, 4) and rotating (2, 3) by 180° about the origin maps it to (−2, −3), so this Year 9 sheet opens with a reflection and a half-turn. The answers record (4, 2), (5, 2) and (6, 8) as mapped points.

Key Takeaways

Section A: Multiple Choice Questions (1 Mark Each)

Choose the correct option for each question.
1. The point (3, 4) is reflected in the y-axis. Where does it map to?
(a) (3, -4)(b) (-3, 4)(c) (-3, -4)(d) (4, 3)
2. A rotation of 180 degrees about the origin maps (2, 3) to which point?
(a) (2, -3)(b) (-2, 3)(c) (-2, -3)(d) (3, 2)
3. A point is translated by the vector (3, -2). The image of (1, 4) is which point?
(a) (4, 2)(b) (-2, 6)(c) (4, -2)(d) (2, 4)
4. Reflecting (5, -2) in the x-axis gives which point?
(a) (-5, -2)(b) (-5, 2)(c) (2, 5)(d) (5, 2)
5. An enlargement of scale factor 2, centre the origin, maps (3, 4) to which point?
(a) (1.5, 2)(b) (9, 12)(c) (6, 8)(d) (6, 4)
6. Which transformation always changes the size of a shape?
(a) Reflection(b) Enlargement(c) Translation(d) Rotation

Section B: Short Answer Type Questions (2 Marks Each)

Show all steps clearly.
7. Describe the single transformation that maps (x, y) to (-x, -y).
8. State the line of reflection that maps (2, 5) to (2, -5).
9. Translate the point (4, -1) by the vector (-2, 5). Give the image.
10. Rotate the point (1, 0) by 90 degrees anticlockwise about the origin.
11. The point (6, 9) is the image of (2, 3) under an enlargement with centre the origin. Find the scale factor.
12. A shape has rotational symmetry of order 4. How many times does it fit onto itself in one full turn?
13. Reflect the point (3, -5) in the y-axis.
14. A reflection in the y-axis followed by a reflection in the x-axis is equivalent to which single transformation?

Section C: Numericals & Word Problems (3 Marks Each)

Apply the concepts to solve the problems. Show all working.
15. A triangle with vertex (0, 0) is translated by the vector (1, 2). Find the coordinates of the image of (0, 0).
16. A square has vertices (1,1), (3,1), (3,3) and (1,3). It is enlarged by scale factor 2 with centre (1, 1). Find the image of vertex (3, 1).
17. A shape is reflected in the line y = x. Where does the point (4, 1) map to?
18. A rotation of 90 degrees clockwise about the origin maps (0, 2) to which point?
19. The point P(2, -3) is translated by the vector (5, 7), then the image is reflected in the x-axis. Find the final coordinates.
20. A triangle with vertices (1,1), (4,1) and (1,5) is enlarged by scale factor 2 with centre (1, 1). Find the area of the image triangle.

Answer Key

1. b) (-3, 4)
2. c) (-2, -3)
3. a) (4, 2)
4. d) (5, 2)
5. c) (6, 8)
6. b) Enlargement
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
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14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
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18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet

People Also Ask

Where does (3, 4) map to when reflected in the y-axis?

(−3, 4), option (b) in this worksheet (Q1).

Where does a 180° rotation about the origin send (2, 3)?

To (−2, −3), option (c) in this worksheet (Q2).

What transformation changes the size of a shape?

An enlargement, option (b) in this worksheet (Q6).

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