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Answer:
The correct options are 1 and 2.
Step-by-step explanation:
The vertices of triangle are S(-4,4), T(-1,4), R(-1,1).
If triangle translated 2 units left,
and then reflected over the y-axis,
The relation between image and preimage is
..... (1)
The vertices of image are
Therefore the vertices of image are S'(6,4),T'(3,4), R'(3,1).
1. A reflection over the y-axis and then a translation 2 units right is defined as
It is equivalent to relation 1, therefore option 1 is correct.
2. A 180 rotation about the origin, then a translation 2 units right, and then a reflection over the x-axis is defined as
It is equivalent to relation 1, therefore option 2 is correct.
3. A reflection over the y-axis and then a translation 2 units left is defined as
It is not equivalent to relation 1, therefore option 3 is incorrect.
4. A 180 rotation about the origin, then a translation 2 units left, and then a reflection over the x-axis is defined as
It is not equivalent to relation 1, therefore option 4 is incorrect.
5. A reflection over the x-axis and then a translation 2 units right is defined as
It is not equivalent to relation 1, therefore option 5 is incorrect.
6. A reflection over the x-axis and then a translation 2 units left is defined as
It is not equivalent to relation 1, therefore option 6 is incorrect.
Therefore the correct options are 1 and 2.