Reflect the shape in the mirror line
Worked Solution & Answer
Equal distance on opposite side of mirror line B1
Answer: Reflected across vertical mirror line
Reflections — Notes & Worked Examples Show / Hide
Explanation:
To describe a reflection fully (2 marks), you must state: (1) the word reflection, and (2) the equation of the mirror line. Know the key mirror lines: the x-axis is y = 0, the y-axis is x = 0, vertical lines are x = k, horizontal lines are y = k, and diagonal lines are y = x or y = −x.
To reflect a shape, draw the mirror line first, then count the perpendicular distance from each vertex to the mirror line and count the exact same distance on the opposite side.
Example 1: Point P(−2, 5) is reflected in the vertical mirror line x = 1. Find the coordinates of P'.
−2 to 1 is 3 right.
3 more right: 1 + 3 = 4.
Answer: (4, 5)
Example 2: Shape A has vertex (1, 4) and its reflected image B has corresponding vertex (4, 1). Describe the transformation.
Coordinates swap: (1, 4) → (4, 1).
Reflection in the line y = x
Reflect shape A in the y-axis
Worked Solution & Answer
Draw the mirror line first, then count the perpendicular squares from each corner to the mirror line and repeat on the other side.
Vertices at (-1, 1), (-4, 1), (-1, 3)
Vertices at (-1, 1), (-4, 1), (-1, 3)
Answer: Vertices at (-1, 1), (-4, 1), (-1, 3)
The diagram shows triangle **A** drawn on a grid.
Kyle reflects triangle **A** in the x-axis to get triangle **B**.
He then reflects triangle **B** in the line y = x to get triangle **C**.
Amy reflects triangle **A** in the line y = x to get triangle **D**.
She is then going to reflect triangle **D** in the x-axis to get triangle **E**.
Amy says that triangle **E** should be in the same position as triangle **C**.
Is Amy correct?
You must show how you get your answer.
He then reflects triangle **B** in the line y = x to get triangle **C**.
Amy reflects triangle **A** in the line y = x to get triangle **D**.
She is then going to reflect triangle **D** in the x-axis to get triangle **E**.
Amy says that triangle **E** should be in the same position as triangle **C**.
Is Amy correct?
You must show how you get your answer.
Worked Solution & Answer
A = (3,3), (4,3), (4,1) M1
Reflect in x-axis -> B = (3,–3), (4,–3), (4,–1)
Reflect B in y = x -> C = (–3,3), (–3,4), (–1,4) (rotation 90° anticlockwise about O) M1
Reflect A in y = x -> D = (3,3), (3,4), (1,4)
Reflect D in x-axis -> E = (3,–3), (3,–4), (1,–4) (rotation 90° clockwise about O)
So Amy is not correct. A1
Reflect in x-axis -> B = (3,–3), (4,–3), (4,–1)
Reflect B in y = x -> C = (–3,3), (–3,4), (–1,4) (rotation 90° anticlockwise about O) M1
Reflect A in y = x -> D = (3,3), (3,4), (1,4)
Reflect D in x-axis -> E = (3,–3), (3,–4), (1,–4) (rotation 90° clockwise about O)
So Amy is not correct. A1
Answer: No; C has vertices (–3, 3), (–3, 4), (–1, 4) whereas E has vertices (3, –3), (3, –4), (1, –4).
(a) Reflect triangle S in the line y = x, label R (2) (b) Translate triangle S by vector (–4, –6), label T (1)
(a) Reflect triangle **S** in the line y = x
Label the new triangle **R**. [2 marks]
Label the new triangle **R**. [2 marks]
(b) Translate triangle **S** by the vector (-4-6)
Label the new triangle **T**. [1 mark]
Label the new triangle **T**. [1 mark]
Worked Solution & Answer
(a)
Swap (x, y) of S(5,3),(6,3),(6,5) → R(3,5),(3,6),(5,6) M1 A1
Answer (a): Triangle R at (3, 5), (3, 6), (5, 6)
(b)
Subtract (4, 6) → T(1,–3),(2,–3),(2,–1) B1
Answer (b): Triangle T at (1, –3), (2, –3), (2, –1)
Shape **A** and shape **B** are drawn on the coordinate grid.
(a) Describe fully the single transformation that maps shape **A** onto shape **B**. [2 marks]
(b) Reflect shape **A** in the line x = -1. [2 marks]
Worked Solution & Answer
(a)
Each vertex of shape A moves 5 units right and 6 units down M1
⇒ Translation by vector (5, −6). C1
⇒ Translation by vector (5, −6). C1
Answer (a): Translation by vector (5, −6).
(b)
Reflect each vertex across the vertical line x = −1: (−2, 1) → (0, 1), (−4, 1) → (2, 1), (−4, 4) → (2, 4), (−3, 4) → (1, 4), (−3, 2) → (1, 2), (−2, 2) → (0, 2). M1 A1
Answer (b): Reflected L-shape with vertices (0, 1), (2, 1), (2, 4), (1, 4), (1, 2), (0, 2)
Here are two triangles on a grid.
Triangle **B** is an enlargement of triangle **A**.
(a) Write down the scale factor of the enlargement. [1 mark]
(b) On the grid, mark with a cross (×) the centre of enlargement. [1 mark]
(b) On the grid, draw the mirror line. [1 mark]
(d) Write down an equation of this mirror line. [1 mark]
y =
Worked Solution & Answer
(a)
Top edge 3 → 6 so scale factor = 2
rays meet at (1, 2) B1
rays meet at (1, 2) B1
Answer (a): 2
(b)
Cross at (1, 2)
Answer (b): Cross at (1, 2)
(b)
Reflection in line y = x B1
Answer (b): Line y = x drawn
(d)
y = x
Answer (d): y = y = x
The diagram shows a shaded shape on a grid.
(a) On the grid, reflect the shape in the line with equation x = 6 [2 marks]
(b) Describe fully the single transformation that maps triangle P onto triangle Q. [3 marks]
Worked Solution & Answer
(a)
Reflect each vertex across x = 6 M1 A1
Answer (a): Vertices at (6, 4), (9, 3), (10, 5), (11, 1)
(b)
Lengths multiplied by 3 M2
rays through corresponding vertices meet at origin (0, 0) C1
rays through corresponding vertices meet at origin (0, 0) C1
Answer (b): Enlargement, scale factor 3, centre (0, 0)
Here is a triangle S drawn on a grid of squares.
(a) On the grid, reflect triangle S in the line with equation x = 5
Label the new triangle T. [2 marks]
Label the new triangle T. [2 marks]
(b) On the grid, reflect triangle T in the line with equation x = 2
Label the new triangle U. [1 mark]
Label the new triangle U. [1 mark]
(c) Describe fully the single transformation that maps triangle S onto triangle U. [2 marks]
Worked Solution & Answer
(a)
T at (4,5), (3,5), (4,7) M1 A1
Answer (a): T at (4,5), (3,5), (4,7)
(b)
U at (0,5), (1,5), (0,7)
Answer (b): U at (0,5), (1,5), (0,7)
(c)
Translation by (-60) M1 C1
Answer (c): Translation by (-60)
(a) Reflect triangle S in y = x, label R (2) (b) Translate S by (–4, –6), label T (1) (c) Describe single transformation mapping P onto Q (2)
(a) Reflect triangle **S** in the line y = x
Label the new triangle **R**. [2 marks]
Label the new triangle **R**. [2 marks]
(b) Translate triangle **S** by the vector (-4-6)
Label the new triangle **T**. [1 mark]
Label the new triangle **T**. [1 mark]
(c) Describe fully the single transformation that maps triangle **P** onto triangle **Q**. [2 marks]
Worked Solution & Answer
(a)
Swap x and y coordinates of S(5,3),(6,3),(6,5) → R(3,5),(3,6),(5,6) M1 A1
Answer (a): Triangle R at (3, 5), (3, 6), (5, 6)
(b)
Subtract (4,6) → T(1,–3),(2,–3),(2,–1) B1
Answer (b): Triangle T at (1, –3), (2, –3), (2, –1)
(c)
Enlargement SF 3 about origin M1 C1
Answer (c): Enlargement, scale factor 3, centre (0, 0)
Here is a coordinate grid.
(a) Draw the image of triangle **A** after a reflection in the line y = -1. [2 marks]
(b) Describe fully the **single** transformation that maps triangle **A** onto triangle **B**. [3 marks]
(c) Complete this statement. [2 marks]
Worked Solution & Answer
(a)
Reflect (1, 1), (3, 1), (1, 4) across y = −1 to get (1, −3), (3, −3), (1, −6). M1 A1
Answer (a): Triangle with vertices (1, -3), (3, -3) and (1, -6)
(b)
Base reduces from 2 to 1 and height from 3 to 1.5, so enlargement with scale factor 1/2. Rays through corresponding vertices (1,1)→(3,4) and (3,1)→(4,4) intersect at (5, 7). M2 C1
Answer (b): Enlargement, scale factor 1/2, centre (5, 7)
(c)
Rotation of 180° about the origin maps (x, y) to (−x, −y), which is an enlargement of scale factor −1 about (0, 0). M1 C1
Answer (c): Scale factor -1 with centre of enlargement (0, 0)