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.

You are watching: Reflection across the x axis rule

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 alsoA"(1,-2), B"(3,-5), and C"(7,-1)

Reflection Notation:rx-axis = (x,-y)ry-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.

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And reflecting over the

*
-axis,
*
coordinate stays the same while the other coordinate becomes negative.