smc-4420-50-Combinations

Transformations, SMB-007

`P(2,3)` is translated 3 units up and 4 units left.

The new point is then reflected in `x`-axis to form point `P^(′)`.

Find the coordinates of `P^(′)`. (2 marks)

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`(-2,-6)`

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`text{1st transformation:}`

`(2,3)\ ->\ (2-4, 3+3)\ ->\ (-2,6)`

`text{2nd transformation (reflection):}`

`(-2,6)\ ->\ P^(′)(-2,-6)`

`P(-3,-5)` is reflected in the `x`-axis and then translated 3 units to the right to form point `P^(′)`.

Find the coordinates of `P^(′)`. (2 marks)

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`(0,5)`

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`text{1st transformation (reflection):}`

`P(-3,-5)\ ->\ (-3,5)`

`text{2nd transformation:}`

`(-3,5)\ ->\ (0,5)`

The point `A(-2, 5)` lies on the Cartesian plane. It is translated five units left and then reflected in the `y`-axis.

Find the coordinates of the final image of `A`. (2 marks)

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`(7,5)`

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`text(1st transformation:)`

`A(-2, 5)\ ->\ (-7,5)`

`text{2nd transformation (reflection):}`

`(-7,5)\ ->\ (7,5)`

The point `P(4, -3)` lies on the Cartesian plane. It is translated four units vertically up and then reflected in the `y`-axis.

Find the coordinates of the final image of `P`. (2 marks)

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`(-4,1)`

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`text(1st transformation:)`

`P(4,-3)\ ->\ (4,1)`

`text{2nd transformation (reflection):}`

`(4,1)\ ->\ (-4,1)`