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### Course: High school geometry > Unit 1

Lesson 3: Translations# Translating points

Let's practice translations on a coordinate plane. A translation is a way to move a point or shape by a certain number of units in a certain direction. For example, we can translate a point by moving it 5 units left and 3 units up. We describe this translation algebraically using the coordinates (x-5, y+3).

## Want to join the conversation?

- l can't understand this make it simple for you to get it(29 votes)
- 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.(107 votes)

- how do i solve the equation when they dont even give me an x and y axis?(13 votes)
- Here are some tips:

Look at the numbers. You are doing addition and subtraction! Remember that moves up and to the right mean adding to the number, and moving down and to the left means subtracting.

Use a number line in your head. This is especially helpful for moving along the x-axis.

If all else fails, draw a graph on a scrap piece of paper.(30 votes)

- I understand this but when i go the quiz I don't understand nothing(12 votes)
- What do they mean by (x,y)→(x−4,y−6)(0 votes)
- Good question! Let's dive in.

When they use '(x,y)→(x-4,y-6)', this means, whatever the point is on at that moment {a.k.a. (x,y)}, is how much you have to move it. For example, let's say 'x,y' is '-5,2'. Then, we move the 'x' (-5) 4 places to the left (because it is negative). Then, for 'y' (2), we move it six places down (because it is negative.

Hope this helps.

Naomi(22 votes)

- I don't understand where "Sal" got all these numbers from. im confused...?(5 votes)
- The numbers he mentioned were, essentially, the coordinates of the points.

Hope this answers your question!(6 votes)

- Why everyone complaining about letters and stuff? It's pretty easy once you listen(6 votes)
- Because, usually, they don't want to listen. But the fact that you are is a very good sign :)(2 votes)

- What happens if one goes left and the other goes up?(5 votes)
- Then it is no longer a translation. For a translation to be possible, all must move the same distance(4 votes)

- these is like a formula(6 votes)
- How do you translate points with the chart(4 votes)
- How will this even help in the real world?(4 votes)

## 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.