We want to see why a circle would have an infinite number of lines of reflection that would carry the circle into itself
First, a line of reflection is, as the name implies, a line that defines the axis of reflection.
A line of reflection would reflect a figure into itself if and only if it divides the figure in exactly two equal parts.
For example for a square, there are 4 lines of reflection that carry the square into itself, these are:
- Two lines that pass throw the midpoints of two opposite sides.
- Two lines that pass throw two opposite vertices.
But in the case of the circle, there are a lot more lines that divide the circle into two equal parts, actually, there are infinite of these lines.
Any line that passes through the center of the circle will divide it into two equal halves, then all of these lines would reflect the circle into itself.
This is why there is an infinite number of lines of reflection that would carry a circle into itself.
If you want to learn more, you can read:
https://brainly.com/question/1398195
