Symmetry

• Two points, P and P₁, are symmetric with respect to line l when they are the same distance from l, measured along a perpendicular line to l. Line l is the axis of symmetry.

Reflections

• Two points symmetric with respect to a line are called reflections of each other across the line. The line is a line of symmetry.

Symmetrya.) A graph with b.) A graph with c.) A graph with x-axis symmetry y-axis symmetry origin symmetry for every (x,y) the for every (x,y) the for every (x,y) the point (x,-y) is also point (-x,y) is also point (-x,-y) is also on the graph. on the graph. on the graph.

Testing for symmetry

• y = x² + 2 • To test for symmetry replace x with –x and y

with –y . • Check to see if the equation is still equivalent

to the original equation. • If it is there is symmetry to that axis. • Try x² + y² = 2

Point Symmetry

• Two points, P and P₁, are symmetric with respect to a point Q when they are the same distance from Q. P₁ is said to be the image of P.

Symmetric with Respect to Origin

• Two points are symmetric with respect to the origin if and only if both their x- and y-coordinates are additive inverses of each other.

• Example: The point symmetric (3, -5) with respect to the origin is (-3, 5)

• What would it be for point (4, -9)?