Question

Reflect the triangle across the y-axis, and then translate the image 5 units down.

Answer 1

Step-by-step answer:

It is a glide reflection.

The order of sliding and reflection is not important if the gliding is parallel to the line of reflection, which is the case here.

So the equivalent is translate five units down, and then reflect over the y-axis.

Note in general that rotations will not be equivalent to an odd number of reflections.  So looking for an equivalent, look for reflection.

Answer 2

Answer:

The correct option is 2.

Step-by-step explanation:

If a figure reflected across the y-axis, then

$(x,y)\rightarrow (-x,y)$

If a figure translated 5 units down, then

$(x,y)\rightarrow (x,y-5)$

It given that we reflect the triangle across the y-axis, and then translate the image 5 units down. So the relation between preimage and image is defined by the rule

$(x,y)\rightarrow (-x,y-5)$

In option 1, Translate 5 units down, and then reflect over the x-axis.

$(x,y)\rightarrow (x,-(y-5))$

In option 2, Translate 5 units down, and then reflect over the y-axis.

$(x,y)\rightarrow (-x,y-5)$

In option 3, Rotate 180° about the origin.

$(x,y)\rightarrow (-x,-y)$

In option 4, Reflect over the x-axis, and then translate 5 units left.

$(x,y)\rightarrow (x-5,-y)$

The final image is the same as image of option 2.

Therefore the correct option is 2.