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High school geometry
Course: High school geometry > Unit 1
Lesson 3: TranslationsTranslating shapes
Learn how to draw the image of a given shape under a given translation.
Introduction
In this article, we'll practice the art of translating shapes. Mathematically speaking, we will learn how to draw the image of a given shape under a given translation.
A translation by is a transformation that moves all points units in the -direction and units in the -direction. Such a transformation is commonly represented as .
Part 1: Translating points
Let's study an example problem
Find the image of under the transformation .
Solution
The translation moves all points in the -direction and in the -direction. In other words, it moves everything 10 units to the left and 5 units up.
Now we can simply go 10 units to the left and 5 units up from .
We can also find algebraically:
Your turn!
Problem 1
Problem 2
Part 2: Translating line segments
Let's study an example problem
Consider line segment drawn below. Let's draw its image under the translation .
Solution
When we translate a line segment, we are actually translating all the individual points that make up that segment.
Luckily, we don't have to translate all the points, which are infinite! Instead, we can consider the endpoints of the segment.
Since all points move in exactly the same direction, the image of will simply be the line segment whose endpoints are and .
Part 3: Translating polygons
Let's study an example problem
Consider quadrilateral drawn below. Let's draw its image, , under the translation .
Solution
When we translate a polygon, we are actually translating all the individual line segments that make up that polygon!
Basically, what we did here is to find the images of , , , and and connect those image vertices.
Your turn!
Problem 1
Problem 2
Challenge problem
The translation mapped . The image, , is drawn below.
Want to join the conversation?
- I dont understand that well without the graph(39 votes)
- I also don't understand this without a graph(28 votes)
- How do you construct a translation with a compass with a point away from the shape?(23 votes)
- ?I dont get it. Can you put it in simpler words?(0 votes)
- Geometry more like Geomystery because I have no idea what's going on (Joke, this is easy)(22 votes)
- I was confused on the last one. Like I moved it 4,-7 but it's still wrong. Can someone help me please?(9 votes)
- The issue is that the question asks you to go from the image back to the preimage. So if the translation from the preimage to the image is <4,-7>, then to go backwards from the image to the preimage, you have to go backwards along the vector <-4,7>.(26 votes)
- This should be less challenging(13 votes)
- without challenges you would be bored(5 votes)
- why doesnt math slay(8 votes)
- i wanna die after i read that(8 votes)
- I need to understand problem 2 on translating line LM and NO(4 votes)
- Here is a strategy:
Move the green line onto the blue line so that you could see it overlapping it. Then move one point of the green line depending on the translation. In problem 2, the translation is (10,0), so it means that you have to move the point 10 units to the right, and 0 units up. Then do the same thing on the other point. Then you are done.(19 votes)
- I have no idea how to do a reverse translation...(6 votes)
- flip the signs, so -4 turns into +4 and 7 into -7(8 votes)
- I was confused on the direction(8 votes)
- I was confused about the direction my dad went.....italics(4 votes)
- why was this made this is to hard curse new math(9 votes)