Hey everyone, it's Justin again. In this lesson we're going to learn about the coordinate notation
used to describe translations. By the end of this lesson, you should be able to use coordinate
notation to describe translations. Remember coordinate notation from a few lessons ago?
If not, you should pause here to go back into notes and refresh your memory.
In this lesson we're going to start by learning how to write coordinate
notation for the two examples from our previous lesson. Then,
we'll complete two additional examples similar to what you'll see in your practice.
This is the first example that we looked at in the previous lesson. Do you remember this problem?
If not, pause the video now and go back in your notes to review what we did here. In this lesson,
we want to write a notation that describes what happened to our points when we translated,
or shifted them. Let's see if we can find any patterns when going from our pre-image coordinates
to our image coordinates. We want to pay specific attention to how the x values and y values change
from A to A' (Prime). So what change do you see in the coordinates when we go from A to A'?
Remember to think of adding and subtracting since this is a translation.
Now check if that same change happens in all the rest of these.
Hopefully you figured out that 2 was subtracted from all the x values
and 4 was subtracted from all the y values. Let's write the coordinate notation for this.
We know that we started with an x value and a y value for each of the points in our pre-image so
once again we write that as (x, y) in parentheses. Then, we draw an arrow to write what happened
to x and y. So what happened to all the x values with going from our pre-image to our image?
2 was subtracted from all of them. We show that by just writing x - 2. Then, we're going to find
a way to write what changes happen to our y values. We know that 4 was subtracted from all
the y values to go from the pre-image to the image so we write that as y - 4. Now we have our answer,
this is the coordinate notation to describe a translation 2 units to the left and 4 units down.
Here's our second example from the previous lesson.
Now our goal is to write a notation that describes what happened
when this pre-image was translated. Pause the video so you could do this problem on your own.
Let's see how you did. We have to find the pattern that takes us from the pre-image coordinates to
the image coordinates. So what change do you see in the coordinates when we go from C to C'?
Now verify that the same change happens in all the rest of these.
The pattern is that 7 was added to all the x values and 1 was added to all the y values.
Now we can write the coordinate notation for this. We always start by writing x and y in parentheses
and an arrow. Now we write what happened to x and y. Since 7 was added to each x-value to go
from the pre-image to the image, we show that by writing x + 7 and since 1 was added to all
the y values on the pre image to get the image, we write that as y + 1. And now we have our answer,
this is the coordinate notation to describe a translation 7 units to the right and 1 unit up.
Now that we've gone back to the examples from our previous lesson and written the notation,
let's take a look at two more examples that'll be very similar to what you'll
see in your practice problems. Here's the first problem. Given the pre-image, G,
and the coordinate notation of the transformation, write the coordinates of the image, G'. What type
of transformation is occurring? Pause the video now and think through this one on your own.
Okay, our coordinate notation tells us that 5 must be subtracted from the x value. Since 2 - 5 is -3,
we write -3 as the x value of the image. Then we go back to our notation and see that 7 is
added to the y value. Our original y value is -1 and when we add 7 we get a new y value of 6.
We can even make a sketch if you want to see how this looks.
Then we can describe in words what happened here. We can say that this transformation
was a translation 5 units to the left and 7 units up. Now we have both parts of our answer.
Here's the last problem for us to try together. It says: Given the image, J', and the coordinate
notation of the transformation, write the coordinates of the pre-image, J. To find the
pre-image, we're going to have to work backwards. Pause the video and see what you can come up with.
Our coordinate notation tells us that x - 3.5 is equal to -1. We can write that as an equation
and solve for x by adding 3.5 to both sides. We place the value we found for x in the beginning
of our pre-image coordinate. We can also see that y + 1.5 is equal to 5.5. We can solve this
by subtracting 1.5 on each side of the equation and we get 4 as the y value in our pre-image.
Setting up equations and solving can help us work backwards to find that pre-image.
That's it for this lesson! Now you can use coordinate notation
to describe translations. See you next time!