Question

answer attempt 1 out of 2
a rotation 180° clockwise about the origin
a reflection over the x -axis
a translation 2 units up
a reflection over the y -axis

Explanation:

Step1: Recall transformation rules

For a point $(x,y)$ rotated 180° clock - wise about the origin, the new point is $(-x,-y)$. For a translation 2 units up, $(x,y)$ becomes $(x,y + 2)$. For a reflection over the $x$-axis, $(x,y)$ becomes $(x,-y)$. For a reflection over the $y$-axis, $(x,y)$ becomes $(-x,y)$.

Step2: Analyze the figure

If we look at the corresponding points of Figure O and Figure P, we can see that for each point $(x,y)$ in Figure O, the corresponding point in Figure P has coordinates $(x,-y)$. This is the rule for reflection over the $x$-axis.

Answer:

A reflection over the $x$-axis