What is axis of symmetry?

The axis of symmetry is a line that divides a figure into two congruent halves that are mirror images of each other. If you were to fold the figure along the axis of symmetry, the two halves would match exactly.

Key aspects of the axis of symmetry include:

• Definition: It's a line that bisects a figure into two identical halves.
• Symmetry: The two halves are symmetrical with respect to the line. This means for every point on one side, there's a corresponding point on the other side, equidistant from the axis.
• Existence: Not all figures have an axis of symmetry. Some have one, some have multiple, and some have none.
• Examples:
  • A square has four axes of symmetry.
  • A rectangle has two axes of symmetry.
  • An isosceles triangle has one axis of symmetry.
  • A circle has infinitely many axes of symmetry, all passing through its center.
• Quadratic Functions: The axis of symmetry for a <a href="https://www.wikiwhat.page/kavramlar/Quadratic%20Functions">quadratic function</a> in the form f(x) = ax² + bx + c is the vertical line x = -b / 2a. This line also represents the x-coordinate of the vertex of the parabola.
• Finding the Axis: Determining the <a href="https://www.wikiwhat.page/kavramlar/Finding%20the%20Axis">finding the axis</a> of symmetry depends on the figure. For shapes, it involves visual inspection or geometric constructions. For functions, formulas (like the one for quadratic functions) are used.