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Transformations, SMB-013

The trapezium `ABCD` is moved to the new position shown by trapezium `SRQP.`

Which of these transformations resulted in the new position?

  1. Rotate `ABCD` 180° clockwise about the origin.
  2. Rotate `ABCD` 270° clockwise about the origin.
  3. Reflect `ABCD` across the `x`-axis, then translate 8 units left.
  4. Reflect `ABCD` across the `y`-axis, then translate 7 units down.
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`C`

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`text(Reflection in the)\ xtext(-axis:)`

`ABCD -> A^{prime}B^{prime}C^{prime}D^{prime}`

`text(Translate 8 units left:)`

`A^{prime}B^{prime}C^{prime}D^{prime} -> SRQP`

`=>C`

Transformations, SMB-009

The point  `P(-1, -4)`  lies on the Cartesian plane. It is reflected in the `x`-axis to form the point `P^(′)`.

Find the coordinates of `P^(′)`.  (1 mark)

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`(-1,4)`

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`text(Reflections in the)\ xtext{-axis:}`

`ytext{-coordinate has opposite sign and}\ xtext{-coordinate is the same.}`

`P(-1,-4)\ ->\ P^(′)(-1,4)`

Transformations, SMB-008

The point  `P(-3, 7)`  lies on the Cartesian plane. It is reflected in the `y`-axis to form the point `P^(′)`.

Find the coordinates of `P^(′)`.  (1 mark)

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`(7,5)`

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`text(Reflections in the)\ ytext{-axis:}`

`xtext{-coordinate has opposite sign and}\ ytext{-coordinate is the same.}`

`P(-3,7)\ ->\ P^(′)(3,7)`