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 the x - axis reflection

The rule for a reflection over the x - axis is $(x,y)\to(x, - y)$. If $Y''=(3,0)$ is the result of a reflection over the x - axis, reversing this gives us the point before the reflection. Since $y = 0$, the point before reflection over the x - axis is also $(3,0)$.

Step2: Reverse the 90 - degree rotation

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

Answer:

$(0,-3)$