Printable · GCSE Higher · ages 14-16

Transformations: rotation, reflection, translation, enlargement worksheet — GCSE Higher

Fifteen questions on "transformations: rotation, reflection, translation, enlargement" — DfE statement G7. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Transformations: rotation, reflection, translation, enlargement worksheet — GCSE Higher

Maths · GCSE Higher · G7 · Transformations: rotation, reflection, translation, enlargement · 15 questions

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1.Shape T has a vertex at (5, 3). T is enlarged by scale factor −1, centre (2, 1). Work out the coordinates of the image of the vertex (5, 3).
(a)(5, 3)
(b)(−1, −1)
(c)(−5, −3)
(d)(9, 5)
2.Shape S has a vertex at (9, 6). It is enlarged by a scale factor of 1/3, centre the origin. Work out the coordinates of the image of this vertex.
(a)(6, 4)
(b)(27, 18)
(c)(3, 2)
(d)(3, 6)
3.Shape S is enlarged by a scale factor of −3 about a fixed centre. Which statement correctly describes the image compared to the original shape?
(a)3 times the size, opposite side, rotated 180°
(b)3 times the size, same side as the original
(c)3 times the size, same orientation, just further away
(d)1/3 the size, opposite side of the centre
4.A photograph is 10 cm wide and 15 cm tall. It is enlarged to make a similar poster that is 40 cm wide. The poster costs £0.80 per centimetre of its height to print, based on its full height. Work out the cost of printing the poster.
(a)£3
(b)£15.20
(c)£12
(d)£48
5.Shape S has an area of 48 cm². It is enlarged by a scale factor of 1/4 to give shape T. Work out the area of shape T.
(a)3 cm²
(b)24 cm²
(c)12 cm²
(d)768 cm²
6.Point E is at (4, 2). It is rotated 180° about the point (1, 1). Work out the coordinates of the image of point E.
(a)(5, 3)
(b)(−4, −2)
(c)(3, 1)
(d)(−2, 0)
7.Postcard P is similar to postcard Q. The 6 cm side of P corresponds to the 15 cm side of Q, and the 8 cm side of P corresponds to a matching side of Q. Work out the length of that matching side of Q.
(a)3.2 cm
(b)16 cm
(c)17 cm
(d)20 cm
8.An enlargement with scale factor 5 maps the point (4, 1) to the point (12, 9). Which of these points is invariant (does not move) under this enlargement?
(a)(−2, −2)
(b)(−2, 1)
(c)(8, 5)
(d)(2, −1)
9.Point B is at (3, 5). It is reflected in the line y = 2. Work out the coordinates of the image of point B.
(a)(3, −4)
(b)(3, −1)
(c)(3, −5)
(d)(−3, 5)
10.Point P(2, 5) is enlarged with centre (2, 1) to give image point P′(2, −7). Work out the scale factor of the enlargement.
(a)−1.4
(b)2
(c)−1/2
(d)−2
11.Triangle A has a vertex at (1, 2). Triangle A is enlarged, centre (1, 1), to give triangle B, whose corresponding vertex is at (1, 5). Work out the scale factor of the enlargement.
(a)3
(b)4
(c)0.25
(d)2.5
12.Triangle T has a vertex A at (4, 6). It is enlarged by a scale factor of −1/2, centre (2, 2). Work out the coordinates of the image of point A.
(a)(3, 4)
(b)(−2, −3)
(c)(1, 0)
(d)(−2, −6)
13.Point A(1, 2) is enlarged to give image point A′(7, −4). The centre of enlargement lies on the x-axis. Work out the scale factor of the enlargement.
(a)−2
(b)3
(c)2
(d)−1/2
14.Triangle T has a vertex at (8, 4). It is enlarged by a scale factor of 1/2, centre (2, 4). Work out the coordinates of the image of this vertex.
(a)(5, 4)
(b)(14, 4)
(c)(8, 2)
(d)(4, 2)
15.Point D is at (3, 7). It is reflected in the line y = x. Work out the coordinates of the image of point D.
y = x
(a)(−7, −3)
(b)(7, 3)
(c)(−3, 7)
(d)(3, −7)

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