Question

1. rotation 180° about the origin
2. rotation 90° counterclockwise about the origin

Explanation:

Step1: Recall rotation rules

For a 180 - degree rotation about the origin, the rule for a point $(x,y)$ is $(x,y)\to(-x,-y)$. For a 90 - degree counter - clockwise rotation about the origin, the rule for a point $(x,y)$ is $(x,y)\to(-y,x)$.

Step2: Assume coordinates of points

Suppose the vertices of the first polygon have coordinates $(x_1,y_1),(x_2,y_2),\cdots$. For the 180 - degree rotation, the new coordinates will be $(-x_1,-y_1),(-x_2,-y_2),\cdots$. For the second polygon with vertices $(x_3,y_3),(x_4,y_4),\cdots$, after 90 - degree counter - clockwise rotation, the new vertices will have coordinates $(-y_3,x_3),(-y_4,x_4),\cdots$.

Step3: Apply rules to draw

Plot the new points obtained from the rotation rules on the coordinate grid to get the rotated polygons.

Since no specific coordinates are given in the image, we can't give numerical results. But the general process for rotation of a polygon about the origin for 180 - degree and 90 - degree counter - clockwise rotations is as described above.

Answer:

For 180 - degree rotation about the origin, use the rule $(x,y)\to(-x,-y)$ for each vertex of the polygon. For 90 - degree counter - clockwise rotation about the origin, use the rule $(x,y)\to(-y,x)$ for each vertex of the polygon and then plot the new polygons.