Question

the graph shows pentagons mnopq and mnopq. which sequence of transformations maps mnopq onto mnopq? a translation left 12 units followed by a rotation 90° counterclockwise around the origin a rotation 90° clockwise around the origin followed by a translation up 6 units a reflection across the x - axis followed by a rotation 90° counterclockwise around the origin

Explanation:

Step1: Analyze translation

The $x$ - coordinates of the vertices of pentagon $MNOPQ$ are greater than those of pentagon $M'N'O'P'Q'$. A translation of 12 units left would decrease the $x$ - coordinates of the points of $MNOPQ$ to match those of $M'N'O'P'Q'$.

Step2: Analyze rotation

After a 90 - degree counter - clockwise rotation about the origin, the transformation rules for a point $(x,y)$ to $( - y,x)$ can be used to check the orientation of the pentagons. The orientation of $MNOPQ$ after a 90 - degree counter - clockwise rotation about the origin and then a 12 - unit left translation matches that of $M'N'O'P'Q'$.

Step3: Check other options

A rotation of 90 degrees clockwise around the origin followed by a translation up 6 units will not map $MNOPQ$ onto $M'N'O'P'Q'$. Also, a reflection across the $x$ - axis followed by a rotation of 90 degrees counter - clockwise around the origin will not result in the correct mapping.

Answer:

A translation 12 units left followed by a 90 - degree counter - clockwise rotation about the origin.