Line Symmetry A line symmetry is a transformation that takes a line segment to itself, with the original and transformed lines aligning in the same relative...
Line Symmetry
A line symmetry is a transformation that takes a line segment to itself, with the original and transformed lines aligning in the same relative positions. There are two main types of line symmetries: reflection and translation.
Reflection involves flipping the line segment over a fixed point, so that it appears as its mirror image. The original and transformed lines are identical, but they are reflected across the line of symmetry.
Translation involves moving the entire line segment along a fixed path, so that it appears to be shifted. The original and transformed lines are shifted relative to each other, but they are not identical.
Rotational Symmetry
A rotational symmetry is a transformation that takes a line segment to a point that is symmetrically related to the original point. Rotational symmetries include rotations around the origin, rotations around the midpoint of the line segment, and rotations around fixed points other than the origin.
A rotation around the origin moves a point around the center of a circle.
A rotation around the midpoint of the line segment moves a point around the center of a circle through the midpoint.
A rotation around a fixed point other than the origin moves a point around the center of a circle through the fixed point.
Examples
A line segment reflected across a line of symmetry is symmetric with respect to that line.
A line segment translated along a line of symmetry is also symmetric with respect to that line.
A line segment rotated around the origin is symmetric with respect to the origin.
A line segment rotated around a point other than the origin is symmetric with respect to that point