Question

the sequence of transformations, $r_{o,90^{circ}}circ r_{x - axis}$, is applied to $\triangle xyz$ to produce $\triangle xyz$. if the coordinates of $y$ are $(3,0)$, what are the coordinates of $y$? y( , )

Explanation:

Step1: Reverse x - axis reflection

The rule for reflecting a point $(x,y)$ over the x - axis is $(x,y)\to(x, - y)$. To reverse this, if the point after reflection over the x - axis and then rotation is $(3,0)$, after reversing the x - axis reflection, the point before x - axis reflection (let's call it $Y'$) is also $(3,0)$ since $0$ is its own opposite.

Step2: Reverse 90 - degree rotation

The rule for rotating a point $(x,y)$ counter - clockwise about the origin by $90^{\circ}$ is $(x,y)\to(-y,x)$. To reverse a $90^{\circ}$ counter - clockwise rotation, we use the rule $(x,y)\to(y, - x)$.
Applying the reverse - rotation rule to the point $(3,0)$, we get $(0,- 3)$.

Answer:

$(0,-3)$