axis of symmetry
The line that divides a graph into two symmetrical parts.
An axis of symmetry is a line or plane that divides a geometric shape into two congruent parts. For a two-dimensional shape, such as a parabola or a circle, the axis of symmetry is a line that passes through the center of the shape and divides it into two symmetric halves.
In particular, for a parabola, the axis of symmetry is a vertical line that passes through the vertex of the parabola. It is a line of reflection symmetry for the parabola, meaning that if you fold the parabola along the axis of symmetry, the two halves will perfectly overlap. The equation of the axis of symmetry for a parabola of the form y = a(x – h)^2 + k is x = h.
For a circle, any diameter of the circle can be considered an axis of symmetry, as it passes through the center and divides the circle into two symmetric halves.
In three-dimensional geometry, an axis of symmetry for a solid shape can be a line or a plane. For example, a cube has many axes of symmetry, including lines passing through opposite vertices or through the centers of opposite faces, as well as planes passing through opposite faces.
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