Question

1. rotation: 180° about the origin

Explanation:

Step1: Identify original vertices

Original vertices from the graph: $(0,-2)$, $(2,-2)$, $(2,0)$, $(0,-1)$

Step2: Apply 180° rotation rule

The rule for 180° rotation about the origin is $(x,y) \to (-x,-y)$.

• For $(0,-2)$: $(-0, -(-2)) = (0,2)$
• For $(2,-2)$: $(-2, -(-2)) = (-2,2)$
• For $(2,0)$: $(-2, -(0)) = (-2,0)$
• For $(0,-1)$: $(-0, -(-1)) = (0,1)$

Answer:

The vertices of the rotated figure are $(0,2)$, $(-2,2)$, $(-2,0)$, $(0,1)$. When plotted, these form the 180° rotation of the original shape about the origin.