A line of the contrary is a line that divides a figure into 2 mirror parts. In the number below, the currently of symmetry division the numbers into mirror images.
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smashville247.netematics that symmetry
smashville247.netematically, a heat of the opposite is a line of reflection that maps any suggest on the figure ago to the figure.
The line the cuts v the significant axis of the ellipse over is a heat of symmetry. When A and also B are reflected across it, they space mapped come A" and also B", additionally on the ellipse. This is true for any suggest on the ellipse.
Not every lines of enjoy are additionally lines of symmetry just because they divide the figure into 2 equal parts. Return the line through the vertices that the rarely often, rarely hexagon below divides it right into two equal parts, that is no a line of symmetry. Allude A top top the hexagon shows to A" which is no on the hexagon.
A heat of symmetry is well-known as a rigid motion (or transformation) in geometry since the number that is reflected across it go not change size or shape and is only "flipped" across the heat of symmetry.
Multiple currently of reflection
A geometric number can have much more than one heat of reflection. An alert the present of reflection crossing at the figure"s center below.
The rarely often, rarely hexagon from over has 2 lines the symmetry.
Any constant polygon has actually the same number of lines that symmetry together its number of its sides.
The concave decagon shown below only has actually 5 present of symmetry even though that is sides have equal length. Just convex polygons have the right to be regular.
A circle has an infinite number of lines of symmetry. Prefer a continuous hexagon, every line of the opposite intersects in ~ the center of the circle.
Symmetry in the coordinate plane
In the name: coordinates plane, the graph of an equation can have symmetry about the x-, y-axis, or some other line.
A graph is claimed to have actually x-axis the contrary if at any time the point, (x, y), is on the graph, climate (x, -y) is likewise on the graph.
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A graph has actually y-axis the contrary if anytime the point (x, y) is on the graph, climate (-x, y) is additionally on the graph.