A line of the contrary is a line the divides a figure into 2 mirror parts. In the figure below, the present of symmetry divide the numbers into mirror images.
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lungemine.comematics the symmetry
lungemine.comematically, a line of the opposite is a heat of reflection that maps any point on the figure earlier to the figure.
The line that cuts v the significant axis of the ellipse over is a heat of symmetry. When A and B are reflected throughout it, they room mapped come A" and also B", additionally on the ellipse. This is true for any point on the ellipse.
Not all lines of have fun are also lines of the opposite just because they divide the number into 2 equal parts. Although the line through the vertices that the rarely often rare hexagon listed below divides it right into two equal parts, that is no a line of symmetry. Suggest A top top the hexagon mirrors to A" i beg your pardon is no on the hexagon.
A heat of symmetry is known as a rigid movement (or transformation) in geometry since the number that is reflected across it walk not readjust size or shape and also is just "flipped" across the line of symmetry.
Multiple lines of reflection
A geometric figure can have an ext than one line of reflection. An alert the lines of reflection intersect at the figure"s center below.
The rarely often, rarely hexagon from above has 2 lines the symmetry.
Any constant polygon has actually the same variety of lines the symmetry together its variety of its sides.
The concave decagon shown below only has actually 5 present of symmetry even though that sides have equal length. Only convex polygons have the right to be regular.
A circle has actually an infinite variety of lines of symmetry. Like a constant hexagon, every line of the contrary intersects in ~ the center of the circle.
Symmetry in the name: coordinates plane
In the coordinate plane, the graph of an equation can have symmetry around the x-, y-axis, or some various other line.
A graph is said to have x-axis symmetry if anytime the point, (x, y), is top top the graph, then (x, -y) is additionally on the graph.
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A graph has y-axis the opposite if at any time the allude (x, y) is on the graph, climate (-x, y) is additionally on the graph.