Question

1. rotation: 90° ccw about the origin

Explanation:

Step1: Recall rotation rule

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

Step2: Identify original points

Let's assume the vertices of the figure in the original position are $(1,1)$, $(1,4)$, $(3,2)$, $(4,4)$.

Step3: Apply rotation rule

For point $(1,1)$: $(-1,1)$; for point $(1,4)$: $(-4,1)$; for point $(3,2)$: $(-2,3)$; for point $(4,4)$: $(-4,4)$.

Answer:

The new coordinates of the vertices of the rotated figure are obtained by applying the rule $(x,y)\to(-y,x)$ to each vertex of the original figure. The new points (assuming original points as above) are $(-1,1)$, $(-4,1)$, $(-2,3)$, $(-4,4)$.