# How to find a reflection image

To find a reflection image of a point or a shape,  there are some rules you can follow although it is not always possible to follow a rule.

First, let us start with all situations where you can just follow a rule to quickly find the location of the reflected image on the coordinate system.

Keep in mind that once you know how to find a reflection image for a point, you can easily find it for a shape. For example, if the shape has 3 points, just find the reflected image for all 3 points and then connect these points with a line.

## How to find a reflection image using the x-axis or the y-axis

Reflection of a point across the x-axis The coordinate of point P is (3, 3) and the coordinate of the reflected image P' is (3, -3)

The coordinate of point A is (-2, 4) and the coordinate of the reflected image A' is (-2, -4)

What do you notice about the x-coordinate and y-coordinate of the preimage and image?

We see that the x-coordinate of the preimage stays the same, but the y-coordinate of the image is the opposite of the y-coordinate of the preimage.

In general, when reflecting a point across the x-axis, if the coordinate of the preimage is (x , y), then the coordinate of the reflected image is (x , -y)

Reflection of a point across the y-axis The coordinate of point P is (-4, 3) and the coordinate of the reflected image P' is (4, 3)

The coordinate of point A is (2, -4) and the coordinate of the reflected image A' is (-2, -4)

What do you notice about the x-coordinate and y-coordinate of the preimage and image?

We see that the y-coordinate of the preimage stays the same, but the x-coordinate of the image is the opposite of the x-coordinate of the preimage.

In general, when reflecting a point across the y-axis,  if the coordinate of the preimage is (x , y), then the coordinate of the reflected image is (-x , y)

## How to find a reflection image using the lines y = x and y = -x

Reflection of a point across the line y = x The coordinate of point P is (1, 4) and the coordinate of the reflected image P' is (4, 1)

The coordinate of point A is (-5, -2) and the coordinate of the reflected image A' is (-2, -5)

Just swap the x-coordinate with the y-coordinate

In general, when reflecting a point across the line y = x,  if the coordinate of the preimage is (x , y), then the coordinate of the reflected image is (y, x)

Reflection of a point across the line y = -x The coordinate of point P is (2, 4) and the coordinate of the reflected image P' is (-4, -2)

The coordinate of point A is (4, -1) and the coordinate of the reflected image A' is (1, -4)

Therefore, swap the x-coordinate with the y-coordinate and then take the opposite of both coordinates.

In general, when reflecting a point across the line y = -x,  if the coordinate of the preimage is (x , y), then the coordinate of the reflected image is (-y, -x)

## Reflection of a point in the origin The coordinate of point P is (5, 2) and the coordinate of the reflected image P' is (-5, -2)

The coordinate of point A is (-2, 3) and the coordinate of the reflected image A' is (2, -3)

Just take the opposite of both coordinates.

In general, when reflecting a point in the origin,  if the coordinate of the preimage is (x , y), then the coordinate of the reflected image is (-x, -y)

When reflecting a point across any line, just keep this mind. The distance between the point and the line and the reflected point and the line is exactly the same.

When reflecting a point A in any point P, just keep this mind these two things.

The distance between point A and point P and the reflected point A' and point P is exactly the same.

Point P, the reflected point A' and point A are colinear.

## Recent Articles 1. ### Basic Math Review Game - Math adventure!

May 19, 19 09:20 AM

Basic math review game - The one and only math adventure game online. Embark on a quest to solve math problems!

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons. Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

## Recent Articles 1. ### Basic Math Review Game - Math adventure!

May 19, 19 09:20 AM

Basic math review game - The one and only math adventure game online. Embark on a quest to solve math problems! 