Which composition transformation occurs in the following? (x,y) →→(y + 5, -x) (1 point)

Question

a reflection across the y-axis and a translation to the right by 5
A 90-degree clockwise rotation and a translation to the right by 5
a reflection across the x-axis and a translation to the left by -5
A 180-degree rotation and a translation to the right by 5

Answer 1

To analyze the transformation \((x,y) \rightarrow (y + 5, -x)\), let's break it down into its components:

1. The first part of the transformation, \((x,y) \rightarrow (y + 5, -x)\), involves two operations:

   • The \(y\) value is being increased by 5, which is a vertical translation upwards.
   • The \(x\) value becomes \(-x\), which is a reflection across the \(y\)-axis.

2. Now let's look at the specific changes:

   • The transformation reflects the point across the \(y\)-axis (because \(x\) becomes \(-x\)).
   • Then the \(y\) value is translated upwards by 5.

Putting this all together, we can describe the sequential transformation as:

• First, a reflection across the \(y\)-axis, and then a translation of 5 units upwards.

None of the options matches this description exactly. However, if we only focus on the transformations and the language used:

• The translation part here can be viewed as combining both transformations that involve reflection and translation. Out of the provided options, the closest would simply indicate reflection and vertical translation.

Ultimately, the correct description would be a reflection across the \(y\)-axis and a translation up by 5, which is not listed exactly among the choices given.

Let's match with closest answers:

• None of the multiple-choice answers given perfectly matches this.

However, recognizing the operations directly:

• The correct input based on what we see would be "a reflection across the y-axis and a translation upwards by 5".

Therefore none of the exact options provided precisely describe the transformation accurately. If an answer must be selected based on standard types of transformations, the most relevant after interpreting accurately would be linked to options indicating the transformations involving reflection and some form of translation.