**Introduction:**

Introduction Graphing is used for plotting the points in the coordinate system. This technique is used for geometric construction like (line, curve etc.), and it is used to find the system growth. Properties of the coordinate graph: To plot the point in h. The symmetric and coordinate graph is defined in below.

## Possibilities of Symmetry and Coordinate Graph:

- The possible types of symmetry are,
- The symmetry graph with coordinate respect to y-axis of the each point (a, b), and (-a, b) on the graph.
- Coordinate Y-axis acts as mirror for the graph. Using the graphing calculator we will show many functions to test for symmetry graphically.

- If the graph is symmetry with respect to x-axis at each point (a, b), and (-a, b) on the graph.
- If the graph is symmetry with respect to the origin at each point (a, b), and (-a, b) on the graph.

Point P on the coordinate graph and draw the line segment of the point PQ through P and the origin this type of origin is the midpoint of PQ, and Q is in the graph.

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## Examples on Symmetry and Coordinate Graphs:

**x-axis Symmetry**

Test the coordinate graph is symmetric with respect to X axis algebraically, we replace all the y’s with -y and see if we get an equivalent expression.

For x-3y = 7

We replace with

x- 3(-y) = 7

Simplifying the equation we get

x + 3y = 7

For

X^{4} – y^{3} = 5

We replace with

X^{4} – (-y)^{3} = 5

Which is equal to the original expression, so

X^{4} – y^{3} = 5

Above equation is symmetric with respect to x-axis.

**y-axis symmetry:**

Test the coordinate graph is symmetric with respect to y axis algebraically, we replace all the x’s with -x and see if we get an equivalent expression.

For

Y = x^{3}

Replace with.

Y = (-x)^{3} = x^{3}

So y = x^{3}

Above equation is symmetric with respect to y axis.

**Origin symmetry:**

Test the coordinate graph is symmetric with respect to origin algebraically we replace both x and y with -x and -y and see if the result is equivalent to the original expression.

For

X = y^{4}

Replace with

(-y) = (-x)^{4}

So

-y = -x^{4} (or) y = x^{4}

Hence

Y = x^{4}

Above equation is symmetric with respect to the origin.