Question

figure i is the result of a transformation on figure h. which transformation would accomplish this? answer a rotation 180° counterclockwise about the origin a translation 8 units to the right and 10 units down a rotation 90° counterclockwise about the origin a rotation 90° clockwise about the origin

Explanation:

Step1: Recall rotation rules

For a 90 - degree counter - clockwise rotation about the origin, the transformation rule for a point $(x,y)$ is $(-y,x)$. For a 90 - degree clockwise rotation about the origin, the rule is $(y, - x)$. For a 180 - degree counter - clockwise rotation about the origin, the rule is $(-x,-y)$. A translation $(a,b)$ moves a point $(x,y)$ to $(x + a,y + b)$.

Step2: Analyze the orientation and position change

Figure $I$ is rotated compared to Figure $H$. The orientation of the triangle has changed in a way that is consistent with a 180 - degree rotation. If we consider a point on Figure $H$, say a vertex, and apply a 180 - degree counter - clockwise rotation about the origin $(-x,-y)$ to its coordinates, it will map to the corresponding vertex on Figure $I$. A translation of 8 units to the right and 10 units down would just move the figure without rotating it. A 90 - degree counter - clockwise or clockwise rotation would change the orientation in a different way than what is shown.

Answer:

A rotation 180° counterclockwise about the origin