Question

1. which sequence of transformations maps a figure back onto itself? reflection over any line rotation 360 degrees translation 5 units scaling by 2

Explanation:

Step1: Analyze reflection

A reflection over a line changes the orientation of a figure (except for some symmetric figures in specific cases). So it may not always map a figure onto itself.

Step2: Analyze rotation

A rotation of \(360^{\circ}\) is equivalent to doing nothing. Because rotating a figure \(360^{\circ}\) around a point brings each point of the figure back to its original position.

Step3: Analyze translation

A translation of 5 units moves the figure 5 units in a particular direction. Unless the figure has a periodicity (which is not a general case for all figures), a translation of 5 units will not map a general figure onto itself.

Step4: Analyze scaling

Scaling by a factor of 2 changes the size of the figure. So it does not map the original figure onto itself.

Answer:

Rotation 360 degrees