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# Translation challenge problem

CCSS.Math:

## Video transcript

a translation acting on the coordinate plane takes the point negative 169 comma 434 to point negative 2 O 3 comma negative 68 what are the coordinates of the image of the point 31 comma negative 529 under this translation and I encourage you to pause this video and try to think about it on your own so let's think about what the change in X that this translation does and the change in Y that this translation does so our change in X our change in X is going to be our ending point our ending point so negative 2 O 3 minus our starting point - negative 169 minus negative 169 and this is the same thing as I'm surrounded in yellow negative 2 O 3 + 169 which is the same thing as 169 - 203 I'm just writing it this way - for my brain to process it which is the same thing as the negative of 203 - 169 and let's see this one is the easiest for my brain to process this is going to be 34 so this is going to be negative 34 that's our change in X now let's think about our change in Y our change in Y is our ending point is negative 68 negative 68 and our starting point is 434 so our ending point minus our starting point - 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 8 plus 4 plus another 12 so that's going to get us to 502 this is going so this is going to be negative 5 oh - so 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 so if we're starting at thirty-one comma negative 529 we're going to end up at we're going to end up at let me write it this way so if we're starting at this point we're starting at 31 coming negative 529 we're going to end up at 31 minus 34 minus 34 that's how much we're going to shift it and negative 529 negative 529 so negative 529 - 502 - 502 so what's this going to be 31 minus 34 is negative 3 and then if we have negative 5 29 minus 502 that's going to be negative 1031 so that is where we end up we end up at the point negative 3 comma negative 1031 under this point gets mapped at this point under this translation