Question

the graph shows rhombuses abcd and abcd. which sequence of transformations maps abcd onto abcd? a rotation 90° clockwise around the origin followed by a translation left 12 units a reflection across the y - axis followed by a rotation 90° counterclockwise around the origin a translation left 8 units followed by a reflection across the x - axis

Explanation:

Step1: Analyze rotation rules

The rule for a 90 - degree clockwise rotation around the origin is $(x,y)\to(y, - x)$. Analyzing the position of the rhombus, a 90 - degree clockwise rotation would change the orientation in a certain way. After rotation, a translation left 12 units can map the rotated figure to the new position.

Step2: Check other options

For the reflection - rotation option, a reflection across the y - axis changes $(x,y)\to(-x,y)$ and then a 90 - degree counter - clockwise rotation $( - x,y)\to(-y,-x)$ which does not match the transformation. For the translation - reflection option, a translation left 8 units and then a reflection across the x - axis also does not match the transformation of the rhombus from ABCD to A'B'C'D'.

Answer:

a rotation 90° clockwise around the origin followed by a translation left 12 units