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:
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)
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 .