All right, welcome to another math video tutorial. What we're going to do in this one is we're going to quickly translate a figure on the coordinate plane. Now when we translate a figure on the coordinate plane that just means we are sliding the figure around. That's all we are doing. Now a quick way to do this is first determine where the current coordinates are of the figure in question.
So for this triangle here point A is located at positive 2 positive 2 so we're going to record those coordinates. So point A is located at 2, 2. Point B is located at 5, 2. And point C is located at positive 2, positive 6. All right, now what I like to do to determine where the new locations of points A, B, and C will be. is I like to take a look at the movement of the x direction and the y direction and take those numbers and add or subtract them directly to the original coordinates.
For example, all of these numbers here are the x values of our points and the second numbers in the parentheses are the y values. Now the problem is saying that we have to move negative 6 in the x direction. So all we have to do is subtract 6 from our x values. So let's go ahead and do that.
So we're going to start with 2 here, and we're going to take 2 and subtract 6, which is negative 4. The next x value is 5, so we're going to take 5 and subtract 6, and that would give us negative 1. And the last x value is 2, and we already had a 2 from the first example, and we know that 2 minus 6 is negative 4. Now the next thing we're going to do is determine what the y values will be. And the problem is telling us that we have to subtract 9 from the y values. Now how do we know we have to take that away from the y values?
It is because it's saying that we have to go backwards 9 in the y direction. So we can think about it as subtracting 9 from the y values. So let's go ahead and take this y value 2 and subtract 9. That would be negative 7. Let's take this 2, which is the same thing as this, so it's going to be negative 7 again.
And then we're going to take 6 and subtract 9, and that will give us negative 3. Now we can see that all values for the coordinates here are negative, which means the points are going to be in quadrant number 3, which is located right here. So let's go ahead and plot these points right here. The new location of point A is going to be at negative 4, negative 7, which is right here.
So I'm going to put A with a little mark by it. A prime, that is the new location of point A. Point B is going to be located at negative 1, negative 7. So this is the new location of B. And the new location of C is at negative 4, negative 3, which is right here. All right, so let's go ahead and take our triangle and slide it negative 6 in the X direction.
Now any negative movement in the X direction is going to be at negative 6. x direction means to the left because the x-axis goes left and right. But if we go to the left, we can see that the numbers are getting more negative. So anything that is a loss or going backwards is to the left.
And anything that is a negative movement on the y-axis or in the y direction will be going downwards. So we're going to slide this triangle a distance of 1 to the left, 2 to the left, 3, 4, 5, 6. So we just move that negative 6 in the x direction. Now we have to move it negative 9 in the y direction. So we go downwards 1, 2, 3, 4, 5, 6, 7, 8, and of course 9. So the way that we just did this is we figured out where the coordinates were going to be first and then we can just put the triangle at those coordinates.
Now, some people just like to look at the coordinate plane and slide their figure over six to the left and then drop it down nine. However, sometimes you might get coordinates that will not fit on your provided coordinate plane. For example, if you had coordinates that were, say, in the hundreds or maybe like 78 and negative 82 or something like that, you would have to use mathematics to determine where the new coordinates would be located.
So in that case, all you would do is take the change in the x direction and apply that change to the x values and you would take the change in the y direction and apply that change to the y values. Hey, I just want to say thanks for checking out this math video. Please don't forget to hit that subscription button and enable notifications so you can be informed as I upload new videos to my channel. Until next time, this is Shea Masonette with Masonette Math.