Transformations

9.An enlargement has scale factor 0.5 and centre (0, 0). A point on the original is (4, 6). What are the coordinates of its image?

10.Which of the following transformations preserves the size of a shape?

11.A shape is enlarged by scale factor 3. If a side of the original is 4 cm, what is the length of the corresponding side on the image?

12.Describe fully the single transformation that maps triangle A onto triangle B, where A has vertices (1,1), (3,1), (3,3) and B has vertices (-1,1), (-3,1), (-3,3).

13.A shape is rotated 90° anti-clockwise about the point (1, 2). The image of point (3, 4) is ( -1, 4). What is the image of point (2, 5)?

14.An enlargement maps a point (2, -1) to (6, -3). What is the scale factor and centre of enlargement?

15.A reflection in the line y = -x maps point (3, 1) to which point?

16.A translation moves a shape 4 units to the right and 3 units down. Which column vector describes this translation?

17.A shape is reflected in the line x = 2. A point on the original shape is at (5, 3). What are the coordinates of its image?

18.A shape is rotated 90° clockwise about the origin. The image of point (3, 1) is (1, -3). What is the image of point (2, 5)?

19.An enlargement has scale factor 2 and centre (0, 0). A point on the original is (3, 4). What are the coordinates of its image?

20.Triangle A has vertices (1, 1), (3, 1), (3, 3). It is translated by vector \begin{pmatrix}-2\\4\end{pmatrix}. What are the coordinates of the image of vertex (3, 3)?

21.A shape is reflected in the line y = -x. The image of point (2, 3) is (-3, -2). What is the image of point (-1, 4)?

22.A shape is rotated 180° about the point (1, 2). The image of point (3, 4) is (-1, 0). What is the image of point (2, 5)?

23.An enlargement maps a point (2, -1) to (6, -3). What is the scale factor?

24.The point (2, 5) is rotated 90° anti-clockwise about the point (1, 2). What are the coordinates of its image?

25.An enlargement maps a point (2, -1) to (6, -3). What is the centre of enlargement?

26.A shape is reflected in the line y = x and then translated by \begin{pmatrix}2\\-1\end{pmatrix}. The image of point (3, 4) is (6, 2). What is the image of point (1, 2)?

27.Which of the following describes a translation?

28.What is the name of the point about which a shape is rotated?

29.A translation is described by the vector \begin{pmatrix} -3 \\ 5 \end{pmatrix}. What does this mean?

30.Which of the following transformations always produces a congruent shape?

31.What is the scale factor if a shape is enlarged to half its original size?

32.A point (3, 4) is reflected in the line x = 1. What are the coordinates of its image?

33.A shape is rotated 90° clockwise about the origin. The image of point (2, 3) is (3, -2). What is the image of point (4, 1)?

34.An enlargement has centre (0, 0) and scale factor 3. A point on the original is (2, -5). What are the coordinates of its image?

35.Which of the following is not a correct description of a transformation?

36.A shape is enlarged by scale factor \frac{1}{3} with centre (0, 0). A side of the original is 9 cm. What is the length of the corresponding side on the image?

37.What is the name of the transformation that moves a shape without rotating or flipping it?

38.Which of the following is the correct vector for a translation that moves a shape 3 units left and 2 units up?

39.A reflection preserves the size and shape of the object.

40.A shape is reflected in the line y = x. What are the coordinates of the image of the point (3, -2)?

41.A rotation of 90° clockwise about the origin maps point (2, 5) to which point?

42.Which of the following transformations always produce a congruent shape? (Select all that apply)

43.Arrange these transformations in the order they are applied to produce the final image: first a translation by \begin{pmatrix} 2 \\ -1 \end{pmatrix}, then a reflection in the y-axis, then a rotation of 90° clockwise about the origin.

44.Match each transformation to its description.

45.Arrange these steps in the correct order to reflect a shape in a vertical line.

46.A shape is enlarged by scale factor 4. If a side of the original is 3 cm, what is the length of the corresponding side on the image?

47.Describe fully the single transformation that maps triangle A with vertices (1, 1), (3, 1), (3, 3) to triangle B with vertices (-1, 1), (-3, 1), (-3, 3).

48.Complete the sentence.

49.A shape is enlarged by scale factor 2.5 with centre (0,0). A point on the original is at (4, 6). What is the x-coordinate of its image?

50.Explain how to find the centre of rotation when given an object and its rotated image.

51.A shape is enlarged by scale factor 4. If a side of the original is 3 cm, what is the length of the corresponding side on the image?

52.A shape is enlarged by scale factor 2.5 with centre (0,0). A point on the original is at (4, 6). What is the x-coordinate of its image?