Question

determine the function rule for each of following:
$r_{0,90^{circ}}$ $(x,y)longrightarrow$ select
$r_{0,180^{circ}}$ $(x,y)longrightarrow$ select
$r_{0, - 90^{circ}}$ $(x,y)longrightarrow$ select
$r_{x - axis}$ $(x,y)longrightarrow$ select
$r_{y - axis}$ $(x,y)longrightarrow$ select

Explanation:

Step1: Recall 90 - degree rotation rule

A 90 - degree counter - clockwise rotation about the origin ($R_{0,90^{\circ}}$) has the rule $(x,y)\to(-y,x)$.

Step2: Recall 180 - degree rotation rule

A 180 - degree rotation about the origin ($R_{0,180^{\circ}}$) has the rule $(x,y)\to(-x,-y)$.

Step3: Recall - 90 - degree rotation rule

A 90 - degree clockwise rotation about the origin ($R_{0, - 90^{\circ}}$) has the rule $(x,y)\to(y,-x)$.

Step4: Recall x - axis reflection rule

A reflection over the x - axis ($r_{x - axis}$) has the rule $(x,y)\to(x,-y)$.

Step5: Recall y - axis reflection rule

A reflection over the y - axis ($r_{y - axis}$) has the rule $(x,y)\to(-x,y)$.

Answer:

$R_{0,90^{\circ}}:(x,y)\to(-y,x)$
$R_{0,180^{\circ}}:(x,y)\to(-x,-y)$
$R_{0,-90^{\circ}}:(x,y)\to(y,-x)$
$r_{x - axis}:(x,y)\to(x,-y)$
$r_{y - axis}:(x,y)\to(-x,y)$