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 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)
2.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)
3.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)
4.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)
5.An enlargement has a scale factor of −2. Priti says the image must be a mirror image of the original shape. Is Priti correct?
(a)No — it's a 180° rotation, not a reflection.
(b)Yes — negative numbers always mean a reflection.
(c)Yes — upside down is the same thing as mirrored.
(d)No — negative factors change size, not orientation.
6.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)
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.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
9.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
10.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)
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.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
13.Triangle J is mapped onto triangle K by a single transformation with centre O. Triangle K is half the size of triangle J and is inverted (turned through 180°). Which of these transformations maps J onto K?
(a)An enlargement, centre O, scale factor −2.
(b)An enlargement, centre O, scale factor −1/2.
(c)A rotation of 180° about O, with no change in size.
(d)An enlargement, centre O, scale factor 1/2.
14.Triangle ABC is similar to triangle PQR. Side AB is 8 cm and corresponds to side PQ, which is 12 cm. Side AC is 6 cm and corresponds to side PR. Work out the length of PR.
(a)16 cm
(b)10 cm
(c)9 cm
(d)4 cm
15.A pinhole camera is set up at a pitch-side stand, with its aperture at the point O = (2, 1) on a grid. Light from the corner F of a triangular flag, at the point (4, 2), passes through the aperture and forms an inverted image on the film behind it. The projection is an enlargement of scale factor −1.5 centred at O. Work out the coordinates of the image of corner F.
(a)(−1, −0.5)
(b)(−6, −3)
(c)(−4, −2)
(d)(5, 2.5)

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