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# Translation challenge problem

A translation acting on the coordinate plane takes the point (-169,434) to point (-203, -68). What are the coordinates of the image of point (31, -529) under this translation?

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Created by Sal Khan.

## Video transcript

Voiceover:A translation acting on the coordinate plane takes a point negative 169 comma 434 to point negative 203 comma negative 68. What are the coordinates of the image of point 31 comma negative 529 under this translation? I encourage you to pause this video and try to think about it on your own. Let's think about what the change in x that this translation does and the change in y that this translation does. Our change in x is going to be our ending point, so negative 203 minus our starting point. Minus negative 169. This is the same thing as, I'll just write it in yellow, negative 203 plus 169 which is the same thing as 169 minus 203 I'm just writing it this way for put my brain to process it, which is the same thing as the negative of 203 minus 169. Let's see this one is the easiest for my brain to process this is going to be 34. This is going to be negative 34 that's our change in x. I was thinking about our change in y. Our change in y is our ending point is negative 68, and our starting point is 434. Our ending point minus our starting point, minus 434 is going to be equal to, so this is just going to be the same thing as the negative of 68 plus 434 and let's see 430 plus 60 is 490, plus another eight plus four, plus another 12 so that's going to get us to 502. This is going to be negative 502. This translation, what it does is it shifts us in the x direction by negative 34 and it shifts us in the y direction by negative 502. If we're starting at 31 comma negative 529, we're going to end up at, let me write it this way, if we're starting at this point, we're starting at 31 comma negative 529 we're going to end up at 31 minus 34 that's how much we're going to shift it and negative 529, so negative 529 minus 502. What's this going to be? 31 minus 34 is negative 3 and then if we have negative 529 minus 502 that's going to be negative 1031. That is where we end up, we end up at the point negative 3 comma negative 1031, under this point gets mapped to this point under this translation.