In this video, you will learn how to do a reflection over the line *y*=*x*.

The line *y=x*, when graphed on a graphing calculator, would appear as a straight line cutting through the origin with a slope of *1*.

When reflecting coordinate points of the pre-image over the line, the following notation can be used to determine the coordinate points of the image:

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

**For example**:

For triangle ABC with coordinate points A(3,3), B(2,1), and C(6,2), apply a reflection over the line *y=x.*

By following the notation, we would swap the x-value and the y-value.

A(3,3), B(2,1), and C(6,2) would turn into

A'(3,3), B'(1,2), and C'(2,6)

## Video-Lesson Transcript

In this lesson, we’ll take a look at reflecting over a line .

First of all, what is a line ?

This is a line that for every value, we get the same value.

will look something like this. A diagonal straight line.

When , . When , . And when , . And so on.

If we have a point, for example, , we’re going to reflect it over. We need to move perpendicular to it.

One side should be perpendicular to the other side.

Our image now is .

All we did was switch the and the values.

For example, if the initial image is .

We have to make a line perpendicular to measure the distance. Then make the same line distance on to the other side.

The reflected point is .

When we reflect over the line , we just switch the values of and .

Let’s look at an example where we’ll reflect triangle ABC over the line using the coordinates.

We know that the rule is the coordinates is going to switch to . We’ll simply switch them.

Let’s graph this now. And draw a triangle.

Now, we have a reflection of triangle over the line to form the image of .