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 coordinatesWe’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 writeNow, 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 isAnd for reflecting over the

-axis isIf you reflect it over the

-axis, coordinate stays the same the other coordinate becomes negative.See more: In Which Part Of The Plant Does Photosynthesis Take Place, Where Does Photosynthesis Take Place

And reflecting over the

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