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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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# Translations review

Review the basics of translations, and then perform some translations.

### What is a translation?

A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.

This translation maps $\mathrm{\u25b3}XYZ$ onto the blue triangle.

The result is a new figure, called the image. The image is congruent to the original figure.

*Want to learn more about different types of transformations? Check out this video.*

## Performing translations

A figure can be moved horizontally along the $x$ axis and vertically along the $y$ axis.

**Example:**

Translate $\mathrm{\u25b3}LMN$ $-4$ units in the $x$ direction and $-2$ units in the $y$ direction.

A translation of $-4$ units in the $x$ direction results in a $4$ units, and a translation of $-2$ units in the $y$ direction results in a $2$ units.

*shift to the left*by*shift down*byThis translation maps $\mathrm{\u25b3}LMN$ onto the triangle below.

*Want to learn more about performing translations? Check out this video.*

## Want to join the conversation?

- do not understand why i am getting translations

wrong when i thought i know how to do it(48 votes)- I know "Right"!(7 votes)

- “Sir this is a Wendy’s”(15 votes)
- ok can i have uhhhhh a grimace shake pls(0 votes)

- Im Still confused after 3 years(14 votes)
- it dont come to my head because it dont give a clear explanation(12 votes)
- It might seem that way but just try to solve it the best you can and you'll eventually learn from your mistakes(0 votes)

- So if you move a point -3 points in the x axis does it move left or right?(7 votes)
- If you move a point -3 in the x direction (not axis), then it moves to the left.(11 votes)

- Honestly, i thought translations, rotations, reflections and dilations would be hard as i just came from 7th grade. Turns out it's easier than the 7th grade math, Lol-

Also, Has math always been this easy or is it just me?(9 votes) - For the people that don’t get it, here’s a summary and I’ll try to make it as simple as possible

Anything that moves left and right is the x-axis

Anything that moves up and down is the y-axis

If you want to find out the translation:

Get your first coordinate and subtract by either x or y and there’s your answer.**X-axis**

If the x of your first coordinate is negative and the x of your second coordinate is positive, it has moved right

If the x of your first coordinate is positive and the x of your second coordinate is negative, it has moved left**Y-axis**

If the y of your first coordinate is positive and the y of your second coordinate is negative, it has moved down

If the y of your first coordinate is negative and the y of your second coordinate is positive, it has moved up(7 votes) - help me am soooo dumb.(7 votes)
- If you have a problem where you must dilate and use transformations to see if one figure is congruent to another, then how would you do that?(4 votes)
- Hi. You can use the rule of three or find a proportion. Both methods work.

Hope I have helped :)(6 votes)

- can translations overlap?(3 votes)
- It depends because if it were fully overlapping then it would no longer be a translation, but if you mean slightly overlap then it can happen(8 votes)