Question

HURRY PLEASE!!!!! Triangle RST is translated 2 units left and then reflected over the y-axis.

I cant post the pictures but the points are on s(-4,4) t(-1,4) r(-1,1)

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

Answer 1

1 and 2 are the correct answers.

Explanation:

Answer 2

The correct options are 1 and 2.

Explanation:

The vertices of triangle are S(-4,4), T(-1,4), R(-1,1).

If triangle translated 2 units left,

`(x,y)\rightarrow (x-2,y)`

and then reflected over the y-axis,

`(x-2,y)\rightarrow (-x+2,y)`

The relation between image and preimage is

`(x,y)\rightarrow (-x+2,y)` ..... (1)

The vertices of image are

`S(-4,4)\rightarrow S'(6,4)`

`T(-1,4)\rightarrow T'(3,4)`

`R(-1,1)\rightarrow 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)\rightarrow (-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)\rightarrow (-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)\rightarrow (-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)\rightarrow (-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)\rightarrow (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)\rightarrow (x+2,-y)`

It is not equivalent to relation 1, therefore option 6 is incorrect.

Therefore the correct options are 1 and 2.