Question

what is a reflection rule that maps the triangle and its image? the reflection rule is $r_t(x,y)=$ where $t$ is the line (type an equation.). (-x,y), (y,x), (-y,x), (-y,-x), (x,y), (y,-x), (x,-y), (-x,-y)

Explanation:

Step1: Observe coordinate - change pattern

When reflecting a point $(x,y)$ over the line $y = -x$, the transformation rule is $(x,y)\to(-y,-x)$. By observing the original triangle (black) and its image (red) in the graph, we can see that the $x$ - coordinate of each point in the original triangle becomes the negative of the $y$ - coordinate of the corresponding point in the image, and the $y$ - coordinate of each point in the original triangle becomes the negative of the $x$ - coordinate of the corresponding point in the image.

Step2: Identify the line of reflection

The line of reflection for the rule $(x,y)\to(-y,-x)$ is the line $y=-x$.

Answer:

$r_t(x,y)=(-y,-x)$ where $t$ is the line $y = -x$