# 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

### 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

### 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

### 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.