# Reflection: Origin

How to find the image under the reflection in the origin: formula, 3 examples, and their solutions.

## Formula

### Formula

The image of a point (x, y)

under the reflection in the origin is

(-x, -y).

Change the signs of both x and y.

## Example 1

### Example

### Solution

The image of (3, 2) is

under the reflection in the origin.

Then the image point is,

change the signs of both x and y,

(-3, -2).

So (-3, -2) is the answer.

### Graph

This is the graph of (3, 2)

and its image

under the reflection in the origin:

(-3, -2).

## Example 2

### Example

### Solution

The image of (-1, 4) is

under the reflection in the origin.

Then the image point is,

change the signs of both x and y,

(1, -4).

So (1, -4) is the answer.

### Graph

This is the graph of (-1, 4)

and its image

under the reflection in the origin:

(1, -4).

## Example 3

### Example

### Solution

The image of [y = (x - 2)^{2} + 1] is

under the reflection in the origin.

Then the image function is,

change the signs of both x and y,

-y = (-x - 2)^{2} + 1.

(-x - 2)^{2}

= (-(x + 2))^{2}

= (x + 2)^{2}

Multiply -1 to both sides.

Then y = -(x + 2)^{2} - 1.

So [y = -(x + 2)^{2} - 1] is the answer.

### Graph

This is the graph of [y = (x - 2)^{2} + 1]

and its image

under the reflection in the origin:

-y = (-x - 2)^{2} - 1.