Which transformations of RST will result in the same image? Check all that apply. a reflection over the y-axis and then a translation 2 units right
a 180° rotation about the origin, then a translation 2 units right, and then a reflection over the x-axis
a reflection over the y-axis and then a translation 2 units left
a 180° rotation about the origin, then a translation 2 units left, and then a reflection over the x-axis
a reflection over the x-axis and then a translation 2 units right
a reflection over the x-axis and then a translation 2 units left

I think sentences 1 and 2

Step-by-step 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.