Question

a.) translation right 8 and up 7
b.) rotation 180 degrees
c.) translation left 4 and down 7
d.) reflection over the y - axis
a.) rotation 90 degrees counterclockwise
b.) rotation 270 degrees
c.) reflection over the x - axis
d.) rotation 90 degrees clockwise
a.) reflection over the y - axis
b.) reflection over the x - axis
c.) translation up 2 units
d.) rotation 90 degrees clockwise

Explanation:

Step1: Recall transformation rules

Translation moves a figure without rotation or reflection. Rotation turns a figure around a point. Reflection flips a figure over a line.

Step2: Analyze first - set of options

For the first set of figures:

• A translation moves every point of a figure the same distance in the same direction. A rotation changes the orientation of the figure around a fixed point. A reflection creates a mirror - image of the figure over a line.
• By observing the first pair of figures, we see that the figure is flipped over the y - axis. When a point $(x,y)$ is reflected over the y - axis, it becomes $(-x,y)$.
• For the second pair of figures, we can see that the figure is rotated 90 degrees counter - clockwise. When a point $(x,y)$ is rotated 90 degrees counter - clockwise about the origin, it becomes $(-y,x)$.
• For the third pair of figures, we observe that the figure is reflected over the x - axis. When a point $(x,y)$ is reflected over the x - axis, it becomes $(x, - y)$.

Answer:

1. D. Reflection over the y - axis
2. A. Rotation 90 degrees counterclockwise
3. B. Reflection over the x - axis