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: First transformation is rotation

The first transformation is $R_{O,- 90^{\circ}}$, which is a $90^{\circ}$ clock - wise rotation about the origin. The rule for a $90^{\circ}$ clock - wise rotation of a point $(x,y)$ about the origin is $(x,y)\to(y, - x)$. Let the coordinates of point $A$ be $(x,y)$. After the rotation, the coordinates of $A'$ are $(y,-x)$.

Step2: Second transformation is reflection

The second transformation is $r_{y - axis}$, which is a reflection across the $y$ - axis. The rule for a reflection of a point $(x,y)$ across the $y$ - axis is $(x,y)\to(-x,y)$. If the coordinates of $A'$ are $(y,-x)$, then the coordinates of $A''$ after reflection across the $y$ - axis are $(-y,-x)$.

However, since we don't know the coordinates of point $A$ in the given problem, we'll assume $A=(a,b)$.

Step1: Calculate $A'$

For a $90^{\circ}$ clock - wise rotation about the origin of point $A=(a,b)$, using the rule $(x,y)\to(y, - x)$, we have $A'=(b,-a)$.

Step2: Calculate $A''$

For a reflection of $A'=(b,-a)$ across the $y$ - axis using the rule $(x,y)\to(-x,y)$, we get $A''=(-b,-a)$.

Answer:

If the coordinates of $A$ are $(a,b)$, the coordinate of $A'$ (after first transformation) is $(b,-a)$; the coordinate of $A''$ (after second transformation) is $(-b,-a)$