smc-4420-45-Rotations

Transformations, SMB-024

Points `P` and `Q`, shown on the Cartesian plane diagram, are rotated 180° about the origin and become points `P^(′)` and `Q^(′)`.

Plot the points `P^(′)` and `Q^(′)` on the diagram. (3 marks)

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`P^(′)(2,1)`

`Q^(′)(-4,2)`

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`text{Rotating 180° = Rotating 90° twice (in either direction)}`

`text{1st 90° rotation (clockwise):}`

`P(-2,-1)\ ->\ (-1,2)`

`Q(4,-2)\ ->\ (-2,-4)`

`text{2nd 90° rotation (clockwise):}`

`(-1,2)\ ->\ P^(′)(2,1)`

`(-2,-4) \ ->\ Q^(′)(-4,2)`

Transformations, SMB-023

Point `Q(3,1)` on the Cartesian plane is rotated 180° about the origin in a clockwise direction to become point `Q^(′)`.

What are the coordinates of `Q^(′)`. (2 marks)

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`Q^(′)(-3,-1)`

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`text{Rotating 180° = Rotating 90° twice (in either direction)}`

`text{1st 90° rotation (clockwise):}`

`Q(3,1)\ ->\ (1,-3)`

`text{2nd 90° rotation (clockwise):}`

`(1,-3)\ ->\ Q^(′)(-3,-1)`

Transformations, SMB-022

Point `A(4,-3)` on the Cartesian plane is rotated 90° about the origin in a clockwise direction to become point `A^(′)`.

What are the coordinates of `A^(′)`. (1 mark)

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`A^(′)(-3,-4)`

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`A^(′)(-3,-4)`

Transformations, SMB-021

Point `P(-3,-7)` on the Cartesian plane is rotated 90° about the origin in an anticlockwise direction to become point `P^(′)`.

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

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`P^(′)(7,-3)`

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`P^(′)(7,-3)`

Transformations, SMB-020

Points `P` and `Q`, shown on the Cartesian plane diagram, are rotated 90° about the origin in a clockwise direction to become points `P^(′)` and `Q^(′)`.

Plot the points `P^(′)` and `Q^(′)` on the diagram. (2 marks)

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Transformations, SMB-019

Points `A` and `B`, shown on the Cartesian plane diagram, are rotated 90° about the origin in an anticlockwise direction to become points `A^(′)` and `B^(′)`.