# Graphing Translations & Finding a Set of Coordinates

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• 0:01 What Is a Translation?
• 0:31 Graphing Translations
• 1:38 Finding a Set of Coordinates
• 2:37 Putting It Together
• 3:18 Lesson Summary
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Lesson Transcript
Instructor: Artem Cheprasov
In this lesson, you're going to learn how to translate figures by counting boxes, find the coordinates of points, and learn how to translate a figure more quickly using simple math.

## What Is a Translation?

Have you ever translated anything? Maybe you translated something from English into Spanish or Russian. Even if you've never translated a language, you may have translated a shape. Basically, you slid an image in one direction or another.

A translation in math is a scenario where every point in a figure is moved the exact same distance and in the same exact direction: without being rotated, reflected, or resized.

Let's see how we graph translations and find their coordinates.

## Graphing Translations

Look at this image (see video). It's a simple rectangle labeled ABCD. Let's find out how we can translate it as follows: (x, y) becomes (x + 7 and y - 5).

What does this mean? This means we move our rectangle +7 units on the horizontal or (x) axis. In other words, we shift it to the right 7 units. It also means we move our rectangle -5 units on the vertical or (y) axis, or simply 5 units down. By moving the rectangle point by point, as you count out the units (boxes) on the graph, it is firmly in the position you see now (see video).

Ok. Let's try another one. Let's move rectangle MATH as follows (x,y) becomes (x - 7 and y + 4).

What do we do here (see video)? Well, now we move every point -7 units on the x-axis. That means we move everything to the left 7 units on the horizontal axis. It also means we move everything +4 units on the y-axis. That means we move everything upwards on the y-axis. Now, you can see where we find the resulting rectangle as a result of this translation on your screen (see video).

## Finding a Set of Coordinates

That wasn't hard, was it? This next section is really easy, too. Let's find out the coordinates of our rectangles.

Let's go back to rectangle ABCD (see video). Remember, coordinates are given by (x, y).

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