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KS3 · Geometry and Measures

KS3.M-G16 Transformations: Reflection and Rotation

AQA KS3.M-G16 · Calculators not allowed · about 60 minutes

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Reflect point P(3, 2) in the y-axis. Write down the coordinates of the image.

(1)

Reflect the triangle with vertices A(1, 1), B(4, 1) and C(1, 3) in the x-axis. Give the coordinates of A', B' and C'.

(2)

Point D is at (-2, 5). Reflect D in the line x = 0 then in the line y = 0. Write the final coordinates.

(1)

Rotate point E(2, 0) 90 degrees anticlockwise about the origin. State the coordinates of the image.

(2)

Rotate point F(0, -3) 180 degrees about the origin. Give the coordinates of the image.

(2)

A square has vertices at (1, 1), (3, 1), (3, 3) and (1, 3). Rotate the whole square 90 degrees clockwise about the origin. Give the new coordinates in any order.

(3)

Describe fully the single transformation that maps triangle T with vertices (2, 1), (4, 1), (2, 4) onto triangle T' with vertices (-1, 2), (-1, 4), (-4, 2).

(2)

A shape is reflected in the line y = x. Point G at (2, 5) is one vertex. Find the coordinates of G' after reflection in y = x.

(2)

Triangle with vertices A(2, 0), B(5, 0), C(2, 4) is rotated 270 degrees anticlockwise about the origin. Give the coordinates of A', B' and C'.

(3)

Reflect the point H(-3, -2) in the line x = -1. Give the coordinates of the image H'.

(2)

A rectangle has corners at (2, -1), (6, -1), (6, 1) and (2, 1). First rotate the rectangle 90 degrees anticlockwise about the origin, then reflect the result in the x-axis. Give the final coordinates of the four vertices.

(3)

Stretch question. The right-angled triangle with vertices P(1, 0), Q(4, 0) and R(1, 3) is first rotated 90 degrees clockwise about the point P(1, 0), then reflected in the line y = 0. Give the coordinates of P', Q' and R' after both transformations.

(4)

Mark scheme · KS3.M-G16 Transformations: Reflection and Rotation

Question 1

B1 (-3, 2) cao
Answer: (-3, 2)

Question 2

M1 correct method: reflect y-values by negating them or show one reflected vertex, oe
A1 A'(1, -1), B'(4, -1), C'(1, -3) cao
Answer: A'(1, -1), B'(4, -1), C'(1, -3)

Question 3

B1 (2, -5) cao
Answer: (2, -5)

Question 4

M1 correct rotation method: (x, y) -> (-y, x) or equivalent
A1 (0, 2) cao
Answer: (0, 2)

Question 5

M1 method: (x, y) -> (-x, -y) or description
A1 (0, 3) cao
Answer: (0, 3)

Question 6

M1 correct map for one or more vertices using (x, y) -> (y, -x) for 90 degrees clockwise
M1 correct mapping for remaining vertices or a consistent set
A1 images: (1, -1), (1, -3), (3, -1), (3, -3) cao (in any order)
Answer: (1, -1), (1, -3), (3, -1), (3, -3)

Question 7

M1 identify type of transformation or show centre/angle partially
A1 rotation 90 degrees anticlockwise about the point (0, 0) oe
Answer: Rotation 90 degrees anticlockwise about the origin (0, 0)

Question 8

M1 method: swap coordinates (x, y) -> (y, x) or equivalent
A1 (5, 2) cao
Answer: (5, 2)

Question 9

M1 correct mapping rule for 270 degrees anticlockwise (x, y) -> (y, -x) or equivalent
M1 apply to at least two points correctly
A1 A'(0, -2), B'(0, -5), C'(4, -2) cao
Answer: A'(0, -2), B'(0, -5), C'(4, -2)

Question 10

M1 method: find horizontal distance from H to the line x = -1 and reflect across it
A1 H' (1, -2) cao
Answer: (1, -2)

Question 11

M1 rotate 90 degrees anticlockwise: (x, y) -> (-y, x) shown for at least one vertex
M1 reflect in x-axis: show y -> -y for at least one rotated vertex
A1 final vertices (1, -2), (1, -6), (-1, -6), (-1, -2) cao (in any order)
Answer: (1, -2), (1, -6), (-1, -6), (-1, -2)

Question 12

M1 method for rotation about P shown, e.g. translate so P is origin and apply rotation rule
M1 apply rotation to at least two points correctly (examples: Q -> (1, -3), R -> (4, 0))
M1 reflect in y = 0 shown (y -> -y) for at least one point
A1 final points P'(1, 0), Q'(1, 3), R'(4, 0) cao (in any order)
Answer: P'(1, 0), Q'(1, 3), R'(4, 0)

Transformations: Reflection and Rotation - Worksheets, Questions and Revision