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 $y? y(square,square)$

Explanation:

Step1: Reverse the x - axis reflection

The transformation $r_{x - axis}$ reflects a point $(x,y)$ to $(x, - y)$. To reverse it, if the point after reflection is $(x,y)$ (in this case, the point $Y''=(3,0)$), the point before reflection is also $(3,0)$ since $0$ is unchanged when multiplied by - 1. Let this point be $Y'=(3,0)$.

Step2: Reverse the 90 - degree rotation

The rotation $R_{O,90^{\circ}}$ rotates a point $(x,y)$ counter - clockwise about the origin by 90 degrees to $(-y,x)$. To reverse it, if the point after rotation is $(x,y)$ (here $Y'=(3,0)$), we use the reverse - rotation formula. Let the original point be $(a,b)$. If $x = 3$ and $y = 0$, then from the reverse - rotation formula $a=x$ and $b=-y$. Substituting $x = 3$ and $y = 0$, we get $a = 0$ and $b=-3$.

Answer:

$(0, - 3)$