Spegellinje

Spegellinje, or line of reflection, is a line in the plane with respect to which a figure can be reflected to produce a mirror image. In such a reflection, every point P not on the spegellinje is mapped to a point P' such that the spegellinje is the perpendicular bisector of the segment PP'. Points on the spegellinje remain fixed under the reflection.

The line of reflection is also called an axis of symmetry for the figure. A figure has a spegellinje if it is symmetric with respect to that line. Reflections are isometries: they preserve distances and angles but reverse orientation. Under a reflection, lines map to lines, and shapes map onto congruent shapes.

Examples help illustrate the concept. For a simple segment AB, the spegellinje is the perpendicular bisector of AB. A rectangle has two spegellinjer, the lines through the midpoints of opposite sides and parallel to those sides. A square has four, corresponding to its four axes of symmetry. A circle has infinitely many spegellinjer: any line through its center is an axis of symmetry.

Determining a spegellinje involves identifying corresponding points under the reflection. If P and P' are corresponding points, the spegellinje is the perpendicular bisector of PP'. Repeated pairs confirm the same line. In practice, you can construct the line by drawing the midpoints and perpendiculars for multiple point pairs or by identifying the fixed points (the line itself) where the figure coincides with its image.

Spegellinje is a fundamental concept in plane geometry, related to symmetry, transformations, and geometric constructions, and is widely used in mathematics, design, and computer graphics.