Answer:
I think sentences 1 and 2
Explanation:
If triangle translated 2 units left, (x,y)-----(x-2,y)
and then reflected over the y-axis, (x-2,y)-----(-x+2,y)
The relation between image and pilgrimage is (x,y)-----(-x+2,y)
The vertices of image are S(-4,4),T(-1,4), R(-1,1)-----S'(6,4),T'(3,4), R'(3,1)
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 (x,y)-----(-x+2,y)
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 (x,y)-----(-x+2,y)
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 (x,y)-----(-x-2,y)
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 (x,y)-----(-x-2,y)
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 (x,y)-----(x+2,-y)
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 (x,y)-----(x+2,-y)
It is not equivalent to relation 1, therefore option 6 is incorrect.
So for that reason im pretty sure the correct options are 1 and 2.