Question

answer a rotation 90° clockwise about the origin a translation 4 units left and 3 units down a rotation 90° counterclockwise about the origin a translation 3 units left and 4 units down

Explanation:

Step1: Recall transformation rules

For a 90 - degree clock - wise rotation about the origin, the transformation rule for a point $(x,y)$ is $(y, - x)$. For a 90 - degree counter - clockwise rotation about the origin, the rule is $(-y,x)$. For a translation $a$ units left and $b$ units down, the rule for a point $(x,y)$ is $(x - a,y - b)$.

Step2: Analyze the figures

Comparing Figure K and Figure J, we can see that the orientation of the triangles has changed. If we consider a general point on Figure K and its corresponding point on Figure J, we find that a 90 - degree counter - clockwise rotation about the origin maps Figure K to Figure J. We can check this by taking a vertex of Figure K, say $(x,y)$, and applying the 90 - degree counter - clockwise rotation rule $(-y,x)$ and seeing that it matches the position of the corresponding vertex on Figure J.

Answer:

A rotation 90° counterclockwise about the origin