Question

the image (green) is the result of a transformation on the pre - image (blue). which transformation would accomplish this? figure j figure k a rotation 90° clockwise about the origin a rotation 90° counterclockwise about the origin a translation 4 units left and 5 units down a translation 5 units left and 4 units down

Explanation:

Step1: Analyze rotation rules

A 90 - degree clockwise rotation about the origin has the rule $(x,y)\to(y, - x)$ and a 90 - degree counter - clockwise rotation about the origin has the rule $(x,y)\to(-y,x)$. The orientation of Figure J and Figure K does not match these rotation rules.

Step2: Analyze translation

For a translation, if we consider a point $(x,y)$ on Figure J. A translation 4 units left and 5 units down means the new point is $(x - 4,y - 5)$. By comparing the vertices of Figure J and Figure K, we can see that this translation rule is correct. For example, if we take a vertex of Figure J say $(3,0)$, after translation 4 units left and 5 units down, we get $(3-4,0 - 5)=(-1,-5)$ which is consistent with the position of the corresponding vertex on Figure K.

Answer:

C. A translation 4 units left and 5 units down