Question

1. for $r_{y = -x}$

$p(x,y)-->p(x,y)$
$p(x,y)-->p(-y,-x)$
$p(x,y)-->p(y,x)$
$p(x,y)-->p(-x,-y)$

Explanation:

Step1: Recall the rule for reflection over the line \(y = -x\)

The formula for reflection of a point \(P(x,y)\) over the line \(y=-x\) is obtained by swapping the \(x\) and \(y\) coordinates and changing their signs.

Let's assume a general point \(P(x,y)\). After reflection over the line \(y =-x\), the new \(x\) - coordinate of the image point \(P'\) is \(-y\) and the new \(y\) - coordinate of the image point \(P'\) is \(-x\).

Answer:

\(P(x,y)\to P'(-y,-x)\) (the second option)