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### Course: High school geometry>Unit 1

Lesson 3: Translations

# Properties of translations

Experimentally verify the effect of geometric translations on segment length, angle measure, and parallel lines.
When you translate something in geometry, you're simply moving it around. You don't distort it in any way. If you translate a segment, it remains a segment, and its length doesn't change. Similarly, if you translate an angle, the measure of the angle doesn't change.
These properties may seem obvious, but they're important to keep in mind later on when we do proofs. To make sure we understand these properties, let's walk through a few examples.

## Property 1: Line segments are taken to line segments of the same length.

Each square in the grid is $1$ unit long.
Translate line segment $\stackrel{―}{ST}$ by $⟨2,-7⟩$.
What is the length of the pre-image—the segment before the translation?
units
What is the length of the image—the segment after the translation?
units

As you can see for yourself, the pre-image and the image are both line segments with the same length. This is true for any line segment that goes under any translation.

## Property 2: Angles are taken to angles of the same measure.

Translate $\mathrm{\angle }MNP$ by $⟨-5,-6⟩$.
Has the measure of the angle changed after the translation?

As you can see for yourself, the pre-image angle and the image angle have the same measure. This is true for any angle that goes under any translation.

## Property 3: Lines are taken to lines, and parallel lines are taken to parallel lines.

Translate the parallel lines $\stackrel{↔}{FG}$ and $\stackrel{↔}{HJ}$ by $⟨-4,3⟩$.
Are the two image lines parallel?

As you can see for yourself, each line is taken to another line, and the image lines remain parallel to each other. This is true for any line—or lines—that go under any translation.

## Conclusion

We found that translations have the following three properties:
• line segments are taken to line segments of the same length;
• angles are taken to angles of the same measure; and
• lines are taken to lines and parallel lines are taken to parallel lines.
This makes sense because a translation is simply like taking something and moving it up and down or left and right. You don't change the nature of it, you just change its location.
It's like taking the elevator or going on a moving walkway: you start in one place and end in another, but you are the same as you were before, right?

## Want to join the conversation?

• Ahhh yes! I need to know angles to do things in my everyday life!
Sees pizza "WAIT! BEFORE YOU EAT THAT WE HAVE TO FIND OUT THE ANGLE OF THE PIZZA!!" -_-
• I know right
• Will this help me in the future
• As a gardener -- no; as a computer scientist -- yes.
• will this help me understand lam 1
• it helps best if you put thought in it and work toward it
• i highly doubt this is highschool geometry... I am in 7th grade
• The High School Geometry course gets harder as you get through it. But, from my personal experiences, as a 7th grader, I was able to get through the course quite easily.
(1 vote)
• Why is my dog sped?
• you chose the dog. Make an inference
• how do you do this i kind of get it and kind of dont so teach me the way
• Hi Miguel,

The key to understanding translations is that we are SLIDING a point or vertices of a figure LEFT or RIGHT along the x-axis and UP or DOWN along the y-axis.

On our x-axis, if the translation number is positive, move that point right by the given number of units, and if the translation number is negative, move that point to its left.

Use the same logic for y-axis; if the translation number is positive, move it up, and if the translation number is negative, move the point down.

Let us have a look at an example. We are given a point A, and its position on the coordinate is (2, 5). The translation number is (-1, 3).

So, we will move the point LEFT by 1 unit on the x-axis, as translation number is (-1).
We will then move the point 3 units UP on the y-axis, as the translation number is (+3).
The image will be A prime at (1, 8).

We did this with a point, but the same logic is applicable when you have a line or any kind of figure.

The other two points to remember in a translation are-
1. Lengths don't change
2. Angles don't change

I hope this helped.

Aiena.
• hello how are y'all doing today
• I'm doing pretty good myself
(1 vote)
• these comments are so old
• The site defaults to showing the top rated questions & answers. Since the rating take time to accumulate, they are apt to be older. You should read them, they likely have good things to learn.

If you want to see the more recent questions, just change the sort sequence to "recent".
• this is differnt then what there teaching us in my class
• The key to understanding translations is that we are SLIDING a point or vertices of a figure LEFT or RIGHT along the x-axis and UP or DOWN along the y-axis.

On our x-axis, if the translation number is positive, move that point right by the given number of units, and if the translation number is negative, move that point to its left.

Use the same logic for y-axis; if the translation number is positive, move it up, and if the translation number is negative, move the point down.

Let us have a look at an example. We are given a point A, and its position on the coordinate is (2, 5). The translation number is (-1, 3).

So, we will move the point LEFT by 1 unit on the x-axis, as translation number is (-1).
We will then move the point 3 units UP on the y-axis, as the translation number is (+3).
The image will be A prime at (1, 8).

We did this with a point, but the same logic is applicable when you have a line or any kind of figure.

The other two points to remember in a translation are-
1. Lengths don't change
2. Angles don't change

I hope this helped.