Question

multiple choice 1 point
if the pentagon below is to be reflected over the y - axis, which point would not move at all?

Explanation:

Step1: Recall reflection rule

When a point $(x,y)$ is reflected over the y - axis, the transformation rule is $(x,y)\to(-x,y)$.

Step2: Analyze each point

For point $G(- 4,0)$, after reflection over the y - axis, it becomes $(4,0)$. It moves.
For point $H(-3,2)$, after reflection over the y - axis, it becomes $(3,2)$. It moves.
For point $J(2,2)$, after reflection over the y - axis, it becomes $(-2,2)$. It moves.
For point $K(2, - 2)$, after reflection over the y - axis, it becomes $(-2,-2)$. It moves.
For point $L(-3,-2)$, after reflection over the y - axis, it becomes $(3,-2)$. It moves.
However, if a point lies on the y - axis, its x - coordinate is 0. When reflected over the y - axis, a point of the form $(0,y)$ remains $(0,y)$. There is no such point in the given pentagon. But if we consider the general concept, a point on the y - axis does not move when reflected over the y - axis. Since there is no point on the y - axis in the given pentagon, all the points of the given pentagon move.

Answer:

None of the points would not move.