Answer:
It is a Translation of (x, y - 2), reflection over y = 1, and 180° rotation about the origin.
Explanation:
To determine the sequence of transformations that will map figure Q onto figure Q', let's analyze the options given:
Option A:
Qª
Translation of (x, y + 2), reflection over x = 1, and 180° rotation about the origin
Option B:
Qª
Translation of (x, y-2), reflection over x = 1, and 180° rotation about the origin
Option C:
Qª
Translation of (x, y-2), reflection over y = 1, and 180° rotation about the origin
Option D:
Qª
Translation of (x, y + 2), reflection over y = 1, and 180° rotation about the origin
To determine the correct sequence, let's break down each transformation:
Translation of (x, y + 2): This moves the figure 2 units up.
Reflection over x = 1: This reflects the figure over the line x = 1. It means that every point (x, y) in the figure will be transformed to (x, 2 - y). This reflects the figure across the line x = 1.
180° rotation about the origin: This rotates the figure 180 degrees counterclockwise around the origin.
Now, let's analyze the options:
Option A: Translation of (x, y + 2), reflection over x = 1, and 180° rotation about the origin
Option B: Translation of (x, y-2), reflection over x = 1, and 180° rotation about the origin
Option C: Translation of (x, y-2), reflection over y = 1, and 180° rotation about the origin
Option D: Translation of (x, y + 2), reflection over y = 1, and 180