Algebra Examples

$2 x - 2 y = 0$

Step 1

There are three types of symmetry:

1. X-Axis Symmetry

2. Y-Axis Symmetry

3. Origin Symmetry

Step 2

If $(x, y)$ exists on the graph, then the graph is symmetric about the:

1. X-Axis if $(x, - y)$ exists on the graph

2. Y-Axis if $(- x, y)$ exists on the graph

3. Origin if $(- x, - y)$ exists on the graph

Step 3

Check if the graph is symmetric about the $x$ -axis by plugging in $- y$ for $y$ .

$2 x - 2 (- y) = 0$

Step 4

Multiply $- 1$ by $- 2$ .

$2 x + 2 y = 0$

Step 5

Since the equation is not identical to the original equation, it is not symmetric to the x-axis.

Not symmetric to the x-axis

Step 6

Check if the graph is symmetric about the $y$ -axis by plugging in $- x$ for $x$ .

$2 (- x) - 2 y = 0$

Step 7

Multiply $- 1$ by $2$ .

$- 2 x - 2 y = 0$

Step 8

Since the equation is not identical to the original equation, it is not symmetric to the y-axis.

Not symmetric to the y-axis

Step 9

Check if the graph is symmetric about the origin by plugging in $- x$ for $x$ and $- y$ for $y$ .

$2 (- x) - 2 (- y) = 0$

Step 10

Simplify each term.

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Step 10.1

Multiply $- 1$ by $2$ .

$- 2 x - 2 (- y) = 0$

Step 10.2

Multiply $- 1$ by $- 2$ .

$- 2 x + 2 y = 0$

Step 11

Multiply both sides by $- 1$ .

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Step 11.1

Multiply each term by $- 1$ .

$- (- 2 x) - (2 y) = - 0$

Step 11.2

Simplify each term.

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Step 11.2.1

Multiply $- 2$ by $- 1$ .

$2 x - (2 y) = - 0$

Step 11.2.2

Multiply $2$ by $- 1$ .

$2 x - 2 y = - 0$

Step 11.3

Multiply $- 1$ by $0$ .

$2 x - 2 y = 0$

Step 12

Since the equation is identical to the original equation, it is symmetric to the origin.

Symmetric with respect to the origin

Step 13