If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Translating points

Translations are defined by saying how much a point is moved to the left/right and up/down.

Want to join the conversation?

  • blobby green style avatar for user Likisha Small
    l can't understand this make it simple for you to get it
    (29 votes)
    Default Khan Academy avatar avatar for user
    • male robot hal style avatar for user John Malig
      You literally just move it. If asked to translate a point (x+1,y+1), you move it to the right one unit because + on the x-axis goes to the right, and move it up one unit, because + on the y-axis goes up. Now, if asked to translate (x-1,y-1) You move it to the left one unit since - on the x-axis goes to the left, and move it down one unit since - on the y-axis goes downwards.
      (89 votes)
  • leaf green style avatar for user Claudia
    how do i solve the equation when they dont even give me an x and y axis?
    (12 votes)
    Default Khan Academy avatar avatar for user
    • starky ultimate style avatar for user Ant
      I do not know what kind of equation you are trying to solve. Could you be more specific if you are referring to a specific equation?
      In the example from the video, you would need a coordinate plane because you need to move a certain amount of distance.

      However, translations can also be defined without the coordinate plane. A certain notation, T {subscript} (line segment AB) {normal} (P), would describe a translation of a given point P by the directed line segment AB. (A directed line segment is the direction and distance of the translation.)
      In other words, point P would travel in the direction of point A to point B, with the same distance as the distance from point A to point B. If you were to draw a line from point P to its image, it would be parallel to line segment AB.

      *The "{subscript}" and "{normal}" refers to how the following part is written and is not actually written in the notation.

      The notation is described in "Translating shapes":
      https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-translations/a/translating-shapes

      Although it does not discuss translations without a coordinate plane, it shows the notation in the "Introduction". Also, the notation in the article refers to moving points and figures on the coordinate plane, but if you replace the subscript with a line segment, you can translate points and figures without a coordinate plane.

      I hope this helps.
      (1 vote)
  • blobby green style avatar for user Allison
    Hi 0w0

    Does anyone know if the Prodigy game is made by the people who made Khan Academy?
    (5 votes)
    Default Khan Academy avatar avatar for user
  • winston default style avatar for user Kirsten Bradburn
    I don't understand where "Sal" got all these numbers from. im confused...?
    (3 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user ll102806
    So it is currently 10/18/21 at pm (Pacific time). How many years will it take for someone to respond to me?
    (2 votes)
    Default Khan Academy avatar avatar for user
  • male robot donald style avatar for user Carroll.Josiah
    What happens if one goes left and the other goes up?
    (3 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user Tifany Andrade
    these is like a formula
    (4 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user Estrada,Melanie
    (x, y) → (x + 7, y - 1)
    (4 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user hz920803
    help me with practice translate point
    (3 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user Laure.....
    I understand this but when i go the quiz I don't understand nothing
    (3 votes)
    Default Khan Academy avatar avatar for user

Video transcript

- [Instructor] 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 this 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 gonna take some point with the coordinates x comma y. And the x coordinate tells me what's my coordinate in the horizontal direction to the left or 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 to 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 here, P has the coordinates, its x coordinate is three, and its y coordinate is negative four. 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 three to the y. So notice, well, 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, I guess you could say this formula, 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, and they'll describe it like this. Translate x units to the left or the right or three units up or down. You'll sometimes see it like this, but just recognize this is just saying just take your x and subtract five from it, 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.