Question

1. reflection across y = -x

Explanation:

Step1: Recall reflection rule

The rule for reflecting a point $(x,y)$ across the line $y = -x$ is $(x,y)\to(-y,-x)$.

Step2: Assume coordinates of points

Let's assume $F(x_1,y_1)$, $G(x_2,y_2)$, $H(x_3,y_3)$ and $I(x_4,y_4)$ are the coordinates of the vertices of the original polygon.

Step3: Apply reflection rule

The new coordinates after reflection will be $F'(-y_1,-x_1)$, $G'(-y_2,-x_2)$, $H'(-y_3,-x_3)$ and $I'(-y_4,-x_4)$. Then plot these new - points on the coordinate plane to get the reflected polygon.

Answer:

Plot the points obtained by applying the rule $(x,y)\to(-y,-x)$ to each vertex of the original polygon.