Combined transformations

The Maths Habit Handout to print

  1. P (1, 3) is reflected to P′ (1, −1). What is the mirror line?

    y = 1

  2. A rotation about (0, 0) takes P (4, 2) to P′ (−2, 4). Give the angle and the direction.

    90° anticlockwise

  3. A triangle has corners (1, 2), (3, 2) and (1, 3). Its image has corners (−2, 5), (0, 5) and (−2, 6). Write the translation vector.

    −33

Make a half turn, then another half turn. Which way are you facing? What about three quarter turns clockwise?

The way you started; the same as one quarter turn anticlockwise

Which single translation?

21 then 3−4 5−3

Which single rotation?

90° clockwise, then 90° clockwise again 180°

Where does the shape end up?

Reflected in the same line twice Where it started
  1. Reflect A in x = 1. Label it B.
  2. Reflect B in x = 4. Label it C.
  3. Describe the single transformation from A to C.
−2−1123456712340ABC
reflectionrotationtranslation
by the vector 60
  1. Reflect A in x = 1. Label it B. (Done for you.)
  2. Reflect B in y = 1. Label it C.
  3. Describe the single transformation from A to C.
−4−3−2−1123456−3−2−1123450ABC
reflectionrotationtranslation
180° about (1, 1)
  1. Reflect A in x = 1. Label it B.
  2. Reflect B in x = 4. Label it C.
  3. Describe the single transformation from A to C.
−2−1123456712340ABC
reflectionrotationtranslation
by the vector 60
  1. Rotate A 90° anticlockwise about (0, 0). Label it B.
  2. Rotate B 90° anticlockwise about (0, 0). Label it C.
  3. Describe the single transformation from A to C.
−4−3−2−11234−3−2−112340ABC
reflectionrotationtranslation
180° about (0, 0)
  1. Reflect A in x = 1. Label it B.
  2. Reflect B in x = 4. Label it C.
  3. Describe the single transformation from A to C.
−2−1123456712340ABC
reflectionrotationtranslation
by the vector 60
  1. Reflect A in y = 2. Label it B.
  2. Reflect B in y = −1. Label it C.
  3. Describe the single transformation from A to C.
−2−11234−4−3−2−1123450ABC
reflectionrotationtranslation
by the vector 0−6
  1. Reflect A in x = 1. Label it B.
  2. Reflect B in x = 4. Label it C.
  3. Describe the single transformation from A to C.
−2−1123456712340ABC
reflectionrotationtranslation
by the vector 60
  1. Translate A by −4−1. Label it B.
  2. Translate B by 36. Label it C.
  3. Describe the single transformation from A to C.
−4−3−2−11234−4−3−2−112340ABC
reflectionrotationtranslation
by the vector −15
  1. Reflect A in x = 1. Label it B.
  2. Reflect B in x = 4. Label it C.
  3. Describe the single transformation from A to C.
−2−1123456712340ABC
reflectionrotationtranslation
by the vector 60
  1. Reflect A in y = 3. Label it B.
  2. Reflect B in x = −3. Label it C.
  3. Describe the single transformation from A to C.
−6−5−4−3−2−11−11234560ABC
reflectionrotationtranslation
180° about (−3, 3)

  1. P (2, 3) is reflected in the x-axis, then in the y-axis. Where does it end up?

    (−2, −3)

  2. P (1, 4) is translated by 32, then by −15. Where does it end up?

    (3, 11)

  3. P (2, 1) is reflected in x = 3, then in x = 5. Where does it end up?

    (6, 1)

  4. A shape is translated by 4−1, then by −41. Where does it end up?

    Where it started

  5. Two 90° anticlockwise rotations about the same centre make which single rotation?

    180°

Combined transformations worksheet, page 1

Answer sheet

  1. P (3, 1) is reflected in the line y = x, then in the x-axis. Which single rotation about (0, 0) does the same?

    90° clockwise

  2. P (1, 2) is reflected in x = 3, then in x = 6. Where does it end up? How far has it moved?

    (7, 2): 6 units

  1. P (4, 1): reflect in the x axis, then translate by −23. Where does it end up?

    (2, 2)

  2. Reflect in y = 1, then in y = 3. Describe fully the single transformation.

    Translation by 04

  3. Rotate 90° anticlockwise, then 180°, both about (0, 0). Describe fully the single transformation.

    Rotation 90° clockwise, centre (0, 0)
Exit tickets to print