Question

which sequence of transformations maps ijkl onto ijkl? a rotation 90° counterclockwise around the origin followed by a translation left 3 units and up 9 units a translation up 8 units followed by a reflection across the line x = -3 a reflection across the line y = -3 followed by a rotation 180° clockwise around the origin

Explanation:

Step1: Recall rotation rules

The rule for a 90 - degree counter - clockwise rotation around the origin is $(x,y)\to(-y,x)$.

Step2: Analyze translation

A translation left 3 units and up 9 units has the rule $(x,y)\to(x - 3,y + 9)$.
Let's assume a point $(x,y)$ on $IJKL$. After a 90 - degree counter - clockwise rotation, it becomes $(-y,x)$. Then after the translation, it becomes $(-y-3,x + 9)$.
We can also check the other transformation options:

• For a translation up 8 units, the rule is $(x,y)\to(x,y + 8)$. Then a reflection across $x=-3$ has a more complex rule and does not match the given transformation.
• For a reflection across $y =-3$ followed by a 180 - degree clockwise rotation around the origin, the combined transformation does not match the given pre - image and image.

Answer:

a rotation 90° counterclockwise around the origin followed by a translation left 3 units and up 9 units