Question

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

Explanation:

Step1: Recall rotation rules

A counter - clockwise rotation of 90° about the origin transforms a point (x,y) to (-y,x). A counter - clockwise rotation of 270° about the origin transforms a point (x,y) to (y, - x). A reflection over the y - axis changes (x,y) to (-x,y) and a reflection over the x - axis changes (x,y) to (x, - y).

Step2: Analyze the orientation of the figures

Figure A and Figure B have different orientations. If we consider a point on Figure A, say the top - most vertex of the polygon in Figure A. By observing the position of the corresponding vertex in Figure B, we note that the transformation is a counter - clockwise rotation of 90° about the origin. When we rotate a figure counter - clockwise 90° about the origin, the x and y coordinates of each point are transformed according to the rule (x,y)→(-y,x), which changes the orientation of the figure as seen from A to B.

Answer:

A counterclockwise rotation of 90° about the origin