Question

can a figure be reflected across three lines of reflection so the image is the original figure? explain. choose the correct answer below. a. no. an odd number of reflections changes the orientation of a figure, so 3 reflections will not result in the original figure. b. yes. it is possible to map a figure onto itself with 3 reflections if the figure has any symmetry, such as a parallelogram. c. yes. it is possible to map a figure onto itself with 3 reflections if the figure is a regular figure, such as an isosceles triangle. d. yes. it is possible to map a figure onto itself with 3 reflections if the figure is a regular figure and has symmetry, such as a square.

Explanation:

Step1: Recall reflection property

A single reflection changes the orientation of a figure. An odd - number of reflections changes the orientation.

Step2: Analyze the situation

We have 3 reflections (an odd number). So, it will change the orientation of the figure and cannot map a figure onto itself in most cases. But for a regular figure with appropriate symmetry, it is possible. For example, a regular hexagon has enough symmetry that 3 well - chosen reflections can map it onto itself.

Answer:

D. Yes. It is possible to map a figure onto itself with 3 reflections if the figure is a regular figure and has symmetry, such as a square.