Question

making predictions with transformations quick check
which transformation would result in the same image as a composition transformation of reflections across the x-axis and then the y-axis? (1 point)

○ a 90-degree rotation
○ a dilation
○ a reflection
● a 180-degree rotation

Explanation:

To determine the equivalent transformation for reflecting a point \((x,y)\) across the \(x\)-axis then the \(y\)-axis:

1. Reflecting \((x,y)\) over the \(x\)-axis gives \((x, -y)\).
2. Reflecting \((x, -y)\) over the \(y\)-axis gives \((-x, -y)\).

A \(180^\circ\) rotation about the origin transforms \((x,y)\) to \((-x, -y)\) (since the rotation formula for \(180^\circ\) is \((x,y) \to (-x, -y)\)).

• A \(90^\circ\) rotation (e.g., counterclockwise) transforms \((x,y)\) to \((-y, x)\), which is not equivalent.
• Dilation scales the figure, not reflecting/rotating, so it is irrelevant.
• A single reflection (e.g., over \(y = x\) or an axis) does not produce \((-x, -y)\) from \((x,y)\).

Answer:

a 180 - degree rotation