1.3 SYMMETRY

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1.3 Symmetry

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Transcript of 1.3 SYMMETRY

Page 1: 1.3 SYMMETRY

1.3Symmetry

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x-Axis Symmetry

A graph is said to be symmetric with respect to the x-axis if for every point (x,y) on the graph, the point (x,-y) is on the graph.

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y-Axis Symmetry

A graph is said to be symmetric with respect to the y-axis if for every point (x,y) on the graph, the point (-x,y) is on the graph.

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origin Symmetry

A graph is said to be symmetric with respect to the origin if for every point (x,y) on the graph, the point (-x,-y) is on the graph.

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Tests for Symmetry

x-axisReplace y by -y in the equation. If an equivalent equation results, the graph is symmetric with respect to the x-axis.

y-axis Replace x by -x in the equation. If an equivalent equation results, the graph is symmetric with respect to the y-axis.

origin Replace x by -x and y by -y in the equation. If an equivalent equation results, the graph is symmetric with respect to the origin.

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Not symmetric with respect to the x-axis.

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Symmetric with respect to the y-axis.

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Not symmetric with respect to the origin.


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