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Lesson 2: Translations

# 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 $\mathrm{△}XYZ$ onto the blue triangle.
The result is a new figure, called the image. The image is congruent to the original figure.

## Performing translations

A figure can be moved horizontally along the $x$ axis and vertically along the $y$ axis.
Example:
Translate $\mathrm{△}LMN$ $-4$ units in the $x$ direction and $-2$ units in the $y$ direction.
A translation of $-4$ units in the $x$ direction results in a shift to the left by $4$ units, and a translation of $-2$ units in the $y$ direction results in a shift down by $2$ units.
This translation maps $\mathrm{△}LMN$ onto the triangle below.

## Practice

Problem 1
Draw the image of $\mathrm{△}ABC$ under a translation by $3$ units to the right and $4$ units down.

Want to try more problems like this? Check out this exercise.

## Want to join the conversation?

• do not understand why i am getting translations
wrong when i thought i know how to do it
• I know "Right"!
• Im Still confused after 3 years
• “Sir this is a Wendy’s”
• ok can i have uhhhhh a grimace shake pls
• it dont come to my head because it dont give a clear explanation
• It might seem that way but just try to solve it the best you can and you'll eventually learn from your mistakes
• So if you move a point -3 points in the x axis does it move left or right?
• If you move a point -3 in the x direction (not axis), then it moves to the left.
• 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?
• 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:

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