Question

figure j is the result of a transformation on figure i. which transformation would accomplish this? answer a rotation 180° clockwise about the origin a translation 2 units to the right and 2 units up a rotation 90° clockwise about the origin a rotation 90° counterclockwise about the origin

Explanation:

Step1: Recall rotation rules

For a 90 - degree clockwise rotation about the origin, the transformation rule for a point $(x,y)$ is $(y, - x)$. For a 180 - degree clockwise rotation about the origin, the rule is $(-x,-y)$. For a translation $a$ units right and $b$ units up, the rule is $(x + a,y + b)$. For a 90 - degree counter - clockwise rotation about the origin, the rule is $(-y,x)$.

Step2: Analyze the figure

Let's take a key point on Figure $I$, say $(4,0)$. After transformation to Figure $J$, its corresponding point is $(0, - 4)$.
If we apply the 90 - degree clockwise rotation rule $(x,y)\to(y, - x)$ to the point $(4,0)$, we get $(0,-4)$.

Answer:

A rotation 90° clockwise about the origin