In this lesson, let’s learn more about translations in the coordinate plane. We are supposed to find the coordinates for the image which the after image of a triangle after the points have been translated using the translation X and Y, we’ll translate it to X + 2 and Y - 1. It’s a translation which means it’s a lateral movement. So the way we do this is, let’s take the triangle and we are given the triangle here A, B and C. let’s first find the coordinates for A, B and C. So what is A? The coordinates of A are X axis is 1, 2, 3, 4, and the negative axis. So, it’s -4 and the Y coordinates are 1 and 2. B, the coordinates are -1, -2, -3, and 1, 2, 3, 4, and the coordinates of C are -1 and +1. These are the original coordinates. If we have translated all of these, if it’s a translation that means we move them to exactly the same distance. All three points are moved the exact same distance. So the way to do this is we take the original value which is X and adds 2 to it. So - 4 becomes - 4 + 2, - 3 became - 3 + 2 because that’s what we’re supposed to do right? X went from X to X + 2 and this one from -1 to -1 + 2. The Y coordinate was 2 and what we have to do is subtract 1 from it. Here the Y coordinate was 4, we subtracted 1 from it here the Y coordinate was 1 we subtracted 1 from it because that’s what we’re supposed to do. Notice all we did was I learned the rule X could now be changed to X + 2. So whatever value of X existed, we add 2 to it. Whatever value existed we add 2 to it to get the new coordinate. Whatever value of Y existed we take away 1 from it. That’s what we've done. So let’s figure out what the new coordinates are. So, A prime, A went to A prime right? So A prime becomes -4 + 2 is -2 and 2 - 1 is 1. B Prime is -3 + 2 is -1 and 4 - 1 is 3 and C prime is -1 + 2 is 1 and 1 - 1 is 0. So now, let’s plot this A prime has -2 and 1 so this is A prime. B prime is -1 and 3 and C prime is 1 and 0 so it is 1 and 0. So if I join them this is my image. This is the image. Notice its translation, B went to B prime, A went to A prime, and C went to C prime. If I was to draw lines connecting B and B prime, A and A prime and C and C prime all heading in the same direction at the same length.