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### Course: 8th grade (Eureka Math/EngageNY) > Unit 2

Lesson 1: Topic A: Definitions and properties of the basic rigid motions- Introduction to geometric transformations
- Identifying transformations
- Identify transformations
- Translations intro
- Translating points
- Translate points
- Translating shapes
- Translating shapes
- Translate shapes
- Determining translations
- Determine translations
- Rotations intro
- Rotating points
- Rotate points (basic)
- Determining rotations
- Determine rotations (basic)
- Reflecting points
- Reflect points
- Reflecting shapes
- Reflecting shapes
- Reflect shapes
- Determining reflections
- Determine reflections
- Translations review
- Rotations review
- Reflections review

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# Determining translations

We can find the translation by figuring out how much the x- and y-coordinates need to change to map one triangle onto the other. We map each point to its corresponding point in the other triangle. Moving left means the translation of x is negative, and moving down means the translation of y is negative..

## Want to join the conversation?

- I can't translate Point B'(6,-5) B(-5,-2)

It doesn't make any sense?(19 votes)- I am not positive about what you are asking, but I will do my best:

B is a point on a graph. It is 5 points to the left of the Y-axis (-5). B is also 2 points below the X-axis (-2). B's coordinates are x:-5 y:-2 or (-5,-2).

B' is a movement of B on the graph. That little apostrophe is how you know it is not the original. B' is 6 points to the right of the Y-axis and 5 points below the X-axis. So B''s coordinates are x:6 and y:-5 or (6,-5).

The difference between these points can be found with subtraction:

X: 6-(-5)=11

B's X coordinate moved 11 units to get to B'.

Y:-5-(-2)=-3

B's Y coordinate moved -3 units to get to B'.

B' is a translation of B by (11,-3)

I hope this helped (:(41 votes)

- If someone says to you "Point Q'(3,2) is the image of Q(6,4) under a translation. Determine the translation." Then what do you do? I think the translation is 3 units to the right and two units up, but Khan Academy says that it is wrong.(11 votes)
- I broke my collar bone 2 days ago in a bicycle accident. Could i have upvotes to help with my pain/anxiety/depression.(1 vote)

- whats B' (-3,-4) is the image of B after a reflection in the y-axis, What are the coordinates of B?

translations(8 votes)- Where are you reflecting?

Like where is the mirror line going and its slope?(9 votes)

- i dont really understand the problem without the graph(10 votes)
- the blue triangle is the preimage and the grey triangle is the triangle that we want the image to match to.(4 votes)

- hey guys if you have a problem this can help

Point A′(2,3) is the image of A(3,−4) under a translation.

Determine the translation.

Use non-negative numbers.(7 votes)- In that case, you will say translate 1 unit to the left and 7 units up instead of (-1,7). Please let me know if that doesn't answer your question.(4 votes)

- Well. That was.... vague, in my opinion.... It didn't really help. Can someone help clear this up? [I have ADHD, so this doesn't stick well for me!](5 votes)
- A translation is just moving a figure to a different place on a coordinate grid. The figure still has the same size, you're just moving it in a different place. Think about you. Say you're in your house but then you go outside. You're "translating" yourself. You're still yourself, you haven't changed anything about yourself but you just changed positions. It's the same thing with figures on a coordinate plane.

Here, Sal translates the blue triangle to fit in the gray triangle. He does this by solving for their coordinates (x,y) (x(horizontal) always comes before the y(vertical)). The triangle moved 7 places to the left. Because he moved left, it's a negative so the x coordinate is -7(If it was to the right then it would be positive). He then moved 4 places down. And because he moved down it's negative so the y coordinate is -4(If he moved up then it would be positive). So we have (-7,-4).

Sorry if this was long and a bit complicated. Tell me if you're still confused and need me to simplify this again. Hope this helps at least.(6 votes)

- Is this program ran in Asia?(4 votes)
- Yes, I think Khan Academy is available anywhere. It should be available in Asia.(5 votes)

- Is anyone else tired?(5 votes)
- yes because school(1 vote)

- could you make it positive?(4 votes)
- Yes, it can be a positive number, but that is only when the translation is going UP rather than down, like it was here.(2 votes)

- this makes no sense(4 votes)

## Video transcript

- [Voiceover] We're asked
to use the translation tool to determine the translation that will map triangle WIN, so this right over here, onto the other triangle. So let's see if we can
translate this thing. So I'm gonna use the translation tool. So I'm gonna start with the translation. So it says translate by, and this is gonna say so
how much do we translate the x coordinates, and how much do we translate the y coordinates? Let's see, if I want to map, if I want to get point W to correspond to this point right over here, which it seems like it should, I would have to go from x equals two, to x equals negative five. So my x would have to decrease by seven, so let me type that in. Negative seven, and then, let's see, on the y side, and we saw that, by just typing in negative seven, here we moved it to the left by seven. And now, in the y axis, I need to move it down by, let's see, one, two, three, four. So my y coordinates, I
move it down by four. And let's see. What happens? And it looks like I was able
to successfully translate it by translating x by negative seven, every point here, every point on this has been shifted
to the left by seven, and has been shifted down by four. And I was able to get onto this triangle. I was able to, through the translation, the image is now in kind
of that target triangle that they asked me to map to, to translate to. We got it right.