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# Translating points

CCSS.Math:

## Video transcript

what we're going to do in this video is look at all of the ways of describing how to translate a point and then to actually translate that point on our coordinate plane so for example they say plot the image of point P under a translation by five units to the left and three units up so let's just do that at first and then we're gonna think about other ways of describing this so we want to go five units to the left so we start right over here we're gonna go one two three four five units to the left and then we're gonna go three units up so that's going to be one two three and so the image of point P I guess would show up right over here after this translation described is way now there are other ways that you could describe this translation here we described it just in plain English by five units to the left and three units up but you could and this will look fancy but as we'll see it's hopefully a pretty intuitive way to describe a translation you could say look I'm going to take some point with the coordinates X comma Y and the x coordinate tells me how what's my coordinate in the horizontal direction to the left to the right and so I want that to be five less so I would say X minus five comma Y and what do we do the y coordinate well we're going to increase it by three we're going to translate three units up so y plus three so all this is saying is whatever x and y coordinates you have this translation will make you take five from the X that's what meaning this is this right over here is five units to the left and then this right over here is saying three units up increase your y-coordinate by three decrease your x-coordinate by five and so let's just test this out with this particular coordinate with this particular point so at this point right over P has the coordinates its x-coordinate is 3 and it's y-coordinate is negative for so let's see how that works if I have three comma negative four and I want to apply this translation what happens well let me just do my coordinates and so I started off with three and negative four and I'm going to subtract five from the three so subtract five here we see that right over there and we're going to add 3 to the Y so notice we're instead of an X now I have a three instead of an X now I have a three instead of a Y now I have a negative four instead of a Y now I have a negative four and so another way of writing this we're going from three comma negative four to three minus five is negative two and negative four plus three is negative one so what are the coordinates right over here well the coordinate of this point is indeed negative two comma negative one so notice how this because you say this formula that the algebraic formula that shows how we map our coordinates how it's able to draw the connection between the coordinates and so you'll see questions where they'll tell you hey plot the image on the blue scribe it like this translate X units to the left of the right or three units up or down you'll sometimes see it like this but just recognize this is just saying to take your X and subtract five format which means move five to the left and this just means take your y coordinate and add three to it which means move three up and sometimes they'll ask you hey what's the new coordinate or sometimes they'll ask you to plot something like that but just realize that it's all the same underlying idea