What composition transformation occurs in the following? (x,y)→(y+5,−x)

Question

(1 point)
Responses

a reflection across the y-axis and a translation down by 5
a reflection across the y -axis and a translation down by 5

a 90-degree clockwise rotation and a translation to the right by 5
a 90-degree clockwise rotation and a translation to the right by 5

a 90-degree counterclockwise rotation and a translation down by 5
a 90-degree counterclockwise rotation and a translation down by 5

a reflection across the x-axis and a translation 5 right

Answer 1

To determine the composition transformation for the mapping \((x,y) → (y+5,−x)\), we will analyze the transformations step-by-step.

1. The transformation takes the first coordinate \(x\) and maps it to \(-x\). This indicates a reflection across the y-axis.
2. The second coordinate \(y\) is mapped to \(y + 5\), which indicates a translation upward by 5 units.

Thus, the total transformation consists of the following:

• A reflection across the y-axis (due to the \(-x\) component).
• A translation upwards by 5 (due to the \(y + 5\) component).

Among the provided options, the one closest to our analysis is:

• a reflection across the y-axis and a translation up by 5.

However, this specific choice isn't present in your options. The correct option, based solely on the transformations listed, is:

a reflection across the x-axis and a translation 5 right

(The provided options may not have a matching response according to the transformations derived). Please verify the provided options.