Question

which sequence of transformations will map figure q onto figure q? translation of (x, y + 2), reflection over x = 1, and 180° rotation about the origin translation of (x, y - 2), reflection over x = 1, and 180° rotation about the origin translation of (x, y - 2), reflection over y = 1, and 180° rotation about the origin translation of (x, y + 2), reflection over y = 1, and 180° rotation about the origin

Explanation:

Step1: Analyze vertical translation

By observing the vertical position of figure Q and Q', figure Q needs to be moved down. A translation of $(x,y - 2)$ will move the figure 2 units down vertically.

Step2: Analyze reflection line

To get the correct orientation after translation, we need to reflect over a vertical line. Reflecting over $x = 1$ is consistent with the horizontal - alignment transformation required.

Step3: Analyze rotation

A $180^{\circ}$ rotation about the origin is a common transformation for re - orienting a figure in a plane. After translation and reflection, a $180^{\circ}$ rotation about the origin will map figure Q onto figure Q'.

Answer:

Translation of $(x,y - 2)$, reflection over $x = 1$, and $180^{\circ}$ rotation about the origin