How do you know if a graph is symmetric with respect to the origin?

Solution:

We will use the concept of symmetry to know if a graph is symmetric with respect to the origin.

Let us see how we will use the concept of symmetry to know if a graph is symmetric with respect to the origin.

A graph is symmetric about the origin if and only if the graph is the same in the 1st and 3rd quadrant or it is the same in the 2nd and 4th quadrant.

To find out symmetry about origin we just have to substitute x by -x and y by -y in the equation of the graph. If the graph does not change, then it is symmetric about the origin. If the curve changes then it is not symmetric about the origin.

Hence, by substituting x by -x and y by -y in the graph, we can know if a graph is symmetric about the origin.

How do you know if a graph is symmetric with respect to the origin?

Summary:

Substitute x by -x and y by -y in the graph and if the graph does not change then it is symmetric about the origin.