Question

Rotations as Functions Quick Check 5 of 55 of 5 Items Question The rotation function mapping for a 90-degree clockwise rotation about the origin is equivalent to which other transformation mapping?(1 point) Responses a 270 degrees counterclockwise rotation a 270 degrees counterclockwise rotation a reflection over the line y=x a reflection over the line y equals x a translation a translation a dilation with a scale factor of 14 a dilation with a scale factor of Start Fraction 1 over 2 End Fraction Skip to navigation page 15 of 15 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

The rotation function mapping for a 90-degree clockwise rotation about the origin can be expressed mathematically. When a point \((x, y)\) is rotated 90 degrees clockwise, its new coordinates become \((y, -x)\).

Now let's analyze the options given:

1. **A 270 degrees counterclockwise rotation** - This transformation is equivalent to a 90-degree clockwise rotation because rotating a point 270 degrees counterclockwise is the same as rotating it 90 degrees clockwise (since 360 - 90 = 270). Thus, this option is correct.

2. **A reflection over the line \(y = x\)** - This transformation changes point \((x, y)\) to \((y, x)\), which is not equivalent to a 90-degree clockwise rotation.

3. **A translation** - Translations shift points but do not rotate them, so this option is incorrect.

4. **A dilation with a scale factor of \(\frac{1}{4}\)** - Dilation changes the size of a shape but does not rotate it; therefore, this option is incorrect.

Based on this analysis, the answer is:
**A 270 degrees counterclockwise rotation.**