Question

what is the rule for the reflection? r_y=x(x, y)→(-y, -x) r_y=-x(x, y)→(-y, -x) r_y=x(x, y)→(y, x) r_y=-x(x, y)→(y, x)

Explanation:

Step1: Recall reflection rules

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

Step2: Analyze the transformation

By observing the positions of the pre - image (triangle ABC) and the image (triangle A'B'C') on the coordinate grid, we can see that the x and y - coordinates of each point are swapped. For example, if a point on the pre - image has coordinates $(x,y)$, the corresponding point on the image has coordinates $(y,x)$. This indicates a reflection over the line $y = x$.

Answer:

$r_{y = x}(x,y)\to(y,x)$