Question

composition function
r_y - axis ∘ r_o, - 90°
type your answer in coordinate form. for example, you can type point a as (5, -2)
what is coordinate of a (after first transformation): select
what is coordinate of a (after second transformation): select

Explanation:

Step1: Recall rotation rule

The first transformation is a rotation of $- 90^{\circ}$ (or $270^{\circ}$ counter - clockwise) about the origin $R_{O,-90^{\circ}}$. The rule for rotating a point $(x,y)$ counter - clockwise about the origin by $270^{\circ}$ is $(x,y)\to(y, - x)$.

Step2: Recall reflection rule

The second transformation is a reflection across the $y$ - axis $r_{y - axis}$. The rule for reflecting a point $(x,y)$ across the $y$ - axis is $(x,y)\to(-x,y)$.

Let's assume the coordinates of point $A$ are $(x,y)$.
After the first transformation ($R_{O,-90^{\circ}}$), the coordinates of $A'$ are $(y,-x)$.
After the second transformation ($r_{y - axis}$) on $A'(y, - x)$, the coordinates of $A''$ are $(-y,-x)$.

Since we don't know the actual coordinates of point $A$ in the given grid, we can only give the general transformation results.

Answer:

What is coordinate of $A'$ (after first transformation): $(y, - x)$
What is coordinate of $A''$ (after second transformation): $(-y,-x)$