Question

which transformation would take figure a to figure b? answer a counterclockwise rotation of 90 about the origin a reflection over the x - axis a counterclockwise rotation of 270 about the origin a reflection over the y - axis

Explanation:

Step1: Analyze reflection characteristics

A reflection over the x - axis changes the sign of the y - coordinates of all points. Figure A and Figure B are not mirror - images over the x - axis. A reflection over the y - axis changes the sign of the x - coordinates of all points. Figure A and Figure B are not mirror - images over the y - axis.

Step2: Analyze rotation characteristics

A counterclockwise rotation of 90° about the origin transforms a point (x,y) to (-y,x). A counterclockwise rotation of 270° about the origin transforms a point (x,y) to (y, - x). By observing the orientation of Figure A and Figure B, we can see that Figure A is rotated 180° about the origin to get Figure B. But among the given options, a counterclockwise rotation of 270° about the origin is the correct transformation as it matches the orientation change from Figure A to Figure B.

Answer:

A counterclockwise rotation of 270 about the origin