Symmetry
•Two points, P and P₁, aresymmetric with respect to line lwhen they are the same distancefrom l, measured along aperpendicular line to l. Line l isthe axis of symmetry.
Reflections
•Two points symmetric with respect to a lineare called reflections of each other across theline. The line is a line of symmetry.
Symmetry
a.) 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 ywith –y .
•Check to see if the equation is still equivalentto 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 withrespect to a point Q when they are the samedistance from Q. P₁ is said to be the image ofP.
Symmetric with Respect to Origin
•Two points are symmetric with respect to theorigin if and only if both their x- and y-coordinates are additive inverses of eachother.
•Example: The point symmetric (3, -5) withrespect to the origin is (-3, 5)
•What would it be for point (4, -9)?