Symmetry

4-3 Symmetry

In this lesson we learned how to check for symmetry about the x-axis, y-axis, origin, and line y=x.

To check for symmetry...

1) About the x-axis:

a) Put a negative in front of y, and simplify.

b) If the new equation matches the original, it is symmetric about the x-axis.

2) About the y-axis:

a) Plug in a (-x).

b) " "

3) About the origin:

a) Plug in a (-x), and put a negative in front of y.

b) " "

4) About y=x:

a) Switch the x and y, and solve for y.

b) " "

Example 1: Is y^2 + xy = 5 symmetric about i. the x-axis, ii. the y-axis, iii. the origin, iv. the line y=x?

i. -y^2 + x - y = 5 = y^2 -xy = -5 --> not symmetric about the x-axis

ii. y^2 (-x)y = 5 = y^2 - xy = 5 --> not symmetric about the y-axis

iii. -y^2 + (-x) -y = 5 = -y^2 + xy = 5 --> not symmetric about the origin

iv. x^2 + yx = 5 --> not symmetric about the line y=x

Example 2: " " y = x^2 +4

i. -y= x^2 + 4 = y= -x^2 - 4 --> not symmetric about the x-axis

ii. y= (-x)^2 + 4 = y= x^2 + 4 --> symmetric about the y-axis

iii. -y= (-x)^2 + 4 = -y= x^2 + 4 = y= -x^2 -4 --> not symmetric about the origin

iv. x= y^2 + 4 = y^2= x - 4 = x= sq. root of x-4 --> not symmetric about the line y=x