Question

choose the correct combination of transformations that would work to get the blue pre - image to end up at the red final image. figure a figure a reflection over y axis and then reflection over x axis 90° cw rotation and then a translation 180° ccw rotation and then a translation reflection over x = 1 line and then translation

Explanation:

Step1: Analyze reflection over Y - axis and then X - axis

If we reflect Figure A over the Y - axis, the x - coordinates of all points change their signs. Then reflecting over the X - axis changes the y - coordinates of all points. This will not result in Figure A' as the orientation and position are not correct.

Step2: Analyze 90° CW rotation and then translation

A 90° clock - wise (CW) rotation about the origin changes the coordinates of a point (x,y) to (y, - x). After rotation, a translation can be applied. By observing the orientation and position of Figure A and Figure A', a 90° CW rotation followed by a translation can map Figure A to Figure A'.

Step3: Analyze 180° CCW rotation and then translation

A 180° counter - clockwise (CCW) rotation about the origin changes the coordinates of a point (x,y) to (-x, - y). This will not result in the correct orientation and position of Figure A' as required.

Step4: Analyze reflection over X = 1 line and then translation

Reflecting over the line X = 1 will not give the correct orientation and position of Figure A' as observed from the figures.

Answer:

90° CW Rotation and then a Translation