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 · Non-calculator · 15 questions

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1.Triangle T has a vertex at (2, 1). It is enlarged by a scale factor of 3, centre (0, 0). Work out the coordinates of the image of this vertex.
(a)(6, 1)
(b)(2, 3)
(c)(5, 4)
(d)(6, 3)
2.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)
3.Shape S is enlarged by scale factor −1, centre (0, 0). Which single transformation has the same overall effect as this enlargement, for every point?
(a)A reflection in the y-axis
(b)A reflection in the x-axis
(c)A rotation of 180° about the origin
(d)No transformation — the shape is unchanged
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.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
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.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)
8.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.
9.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
10.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)
11.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
12.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
13.Triangle T has a vertex A at (3, 1). It is enlarged by a scale factor of −2, centre (1, 1). Work out the coordinates of the image of point A.
(a)(−6, −2)
(b)(5, 1)
(c)(−3, 1)
(d)(2, 1)
14.A postcard measuring 10 cm by 15 cm is enlarged by a scale factor of 2 to make a poster. Work out the area of the poster, in cm².
(a)300 cm²
(b)204 cm²
(c)150 cm²
(d)600 cm²
15.Shape S has an area of 5 cm². Shape S is enlarged by a scale factor of −3 to give shape T. Work out the area of shape T.
(a)−15 cm²
(b)45 cm²
(c)9 cm²
(d)15 cm²

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