Question

answer a rotation ( 180^circ ) counterclockwise about the origin a translation 8 units to the right and 10 units down a rotation ( 90^circ ) counterclockwise about the origin a rotation ( 90^circ ) clockwise about the origin

Explanation:

Step1: Identify vertices of Figure H

Vertices: $(-4, 5)$, $(-2, 2)$, $(0, 4)$

Step2: Apply 180° rotation rule

Rule: $(x,y)\to(-x,-y)$
New points: $(4, -5)$, $(2, -2)$, $(0, -4)$

Step3: Match to Figure I vertices

Figure I vertices: $(4, -5)$, $(2, -2)$, $(0, -4)$; matches rotated points.

Answer:

A rotation $180^\circ$ counterclockwise about the origin