In this video, you will learn how to do a reflection over an axis, such as the x-axis or y-axis.

To reflect a shape over an axis, you can either match the distance of a point to the axis on the other side of using the reflection notation.

To match the distance, you can count the number of units to the axis and plot a point on the corresponding point over the axis.

You can also negate the value depending on the line of reflection where the x-value is negated if the reflection is over the y-axis and the y-value is negated if the reflection is over the x-axis.

Either way, the answer is the same thing.

**For example:
**Triangle ABC with coordinate points A(1,2), B(3,5), and C(7,1). Determine the coordinate points of the image after a reflection over the x-axis.

Since the reflection applied is going to be over the x-axis, that means negating the y-value. As a result, points of the image are going to be:

A'(1,-2), B'(3,-5), and C'(7,-1)

By counting the units, we know that point A is located two units above the x-axis. Count two units below the x-axis and there is point A’. Do the same for the other points and the points are also

A'(1,-2), B'(3,-5), and C'(7,-1)

**Reflection Notation:**

r_{x-axis} = (x,-y)

r_{y-axis} = (-x,y)

## Video-Lesson Transcript

In this lesson, we’ll go over reflections on a coordinate system. This will involve changing the coordinates.

For example, try to reflect over the -axis.

We have triangle with coordinates

We’re going to reflect it over the -axis. We’re going to flip it over.

So we’ll do what we normally do. Just one point at a time.

Now, is above units from the -axis so we’ll move it below the -axis by units.

This will be the .

Let’s do the same for . It’s units above the -axis so we’re going to go units below the -axis. Notice that it’s still in line with .

This is now .

Look at point at . It’s point above the -axis so we’ll go point below the -axis.

So, .

And just connect the points. Then we can see our reflection over the -axis.

When we reflect over the -axis, something happens to the coordinates.

The initial coordinates change. The coordinate stays the same but the coordinate is the same number but now it’s negative.

In reflecting over the -axis, we’ll write

Now, the same thing goes for reflecting over the -axis.

We’re going to reflect triangle over the -axis.

Similar to reflecting over the -axis, we’ll just do one point at a time.

is unit from the -axis so we’ll move beyond the -axis.

So, .

Let’s look at at . That means it’s units from the -axis so we’ll move coordinates on the other side of the -axis.

Now, .

Finally, is at so we’ll go points beyond the -axis.

We’ll have .

Now, we can draw a triangle that is a reflection of triangle over the -axis.

Let’s look at how these coordinates changed.

Originally we have coordinates but became negative while stayed the same.

Let’s recap.

The rule of reflecting over the -axis is

And for reflecting over the -axis is

If you reflect it over the -axis, coordinate stays the same the other coordinate becomes negative.

And reflecting over the -axis, coordinate stays the same while the other coordinate becomes negative.