# Top 17 what is a translation in math

Here are the best information about what is a translation in math voted by users and compiled by us, invite you to learn together

In the 19th century, Felix Klein proposed a new perspective on geometry known as transformational geometry. Most of the proofs in geometry are based on the transformations of objects. There are four types of transformations possible for a graph of a function (and translation in math is one of them). They are:

• Rotations
• Translations
• Reflections
• Dilation

In this chapter, we will learn about translation in mathematics using translation math definition and translation math examples. Do try your hand at a few translation math problems on translation geometry at the end of the page.

1. What is Translation in Math? 2. Preimages and Images of Translation 3. Translations on the Coordinate Plane 4. How to Graph Translations in Math? 5. Translations of Functions 6. Translation Represented by a Column Vector or Matrix 7. FAQs on Translations Math

### Translation Math Definition

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions. Since it is just moving of the shape from one place to other, there is no change in the shape.

The direction or the path of this change in position of the object can vary i.e., initially the object can move left, then turn right, and so on. While translating, all the points on the shape will shift by the same number of units. For example, if one point shifts 2 units to the right, then all the points will also move 2 units to the right.

Translation is one of the transformations in math. When a shape has been transformed, the original shape is called the preimage and the vertices are usually labeled using uppercase letters (Example: ABCD). The translated shape is called the image and the vertices are labeled using uppercase letters with a “prime” next to each (Example: A′B′C′D′, and is pronounced “A-prime, B-prime, C-prime, D-prime”).

### Translation in Geometry Example

In the below figure, the preimage is ABC and its image is A’B’C’. Here, ABC is translated in the following two ways (one after the other) to form A’B’C’.

• Moved up (vertically) by 3 units and then
• Moved right (horizontally) by 2 units Note that while translating the triangle to the left/right/up/down, we moved all the points of the triangle by an equal number of units in the same direction.

As we have just seen, a shape before translations are applied is known as “preimage” and the shape that is obtained after the application of translations is known as “image. In simple words:

• “Preimage” is the shape before translation.
• “Image” is the shape after translation.

Look at the following figure where ABCD is the preimage and A’B’C’D’ is the image of ABC. Any object represented in the coordinate plane can be translated horizontally (left/right) or vertically (up/down). Let us look at the last example to understand translations on the coordinate plane. A graph is represented in the coordinate plane as shown in the figure. While translating, the quadrilateral is shifted 5 units horizontally to the right and 1 unit vertically upward, which means the new translated function for the given figure would be

(x, y) → (x + 5, y + 1)

By this time, you might have got an understanding of the process of writing the translations. Left/right affect the x-coordinate and up/down affect the y-coordinate of a point. Here are the rules of translations.

### Translation Rules

• When the shape is moved towards the left by k units, then replace x with x – k.
• When the shape is moved towards the right by k units, then replace x with x + k.
• When the shape is moved up by k units, then replace y with y + k.
• When the shape is moved down by k units, then replace y with y – k.

Example: What are the new coordinates when the translation (x, y) → (x – 2, y + 3) is applied to the point (2, 5).

Solution:

The coordinates of old point (preimage) are (x, y) = (2, 5). Now, applying the given transoformation to this point,

x – 2 = 2 – 2 = 0 y + 3 = 5 + 3 = 8

Thus, the coordinates of the translated point (image) are (0, 8).

To graph the translation of a shape, we follow the steps below:

• Identify the vertices of the shape.
• Apply the given transformation on each of the vertices to find the new vertices (as shown in the above example).
• Then just plot the new points on the coordinate plane and join them as per the given shape.

Example: A shape is formed with vertices (1, 8), (−3, −5), (−4, 7), and (−6, −2). Plot the image of this shape with respect to the translation (x, y) → (x + 6, y + 1).

Solution:

Let us compute the new coordinates of each of the given vertices.

Old Coordinates (Before the Translation) New Coordinates (After the Translation) A (1, 8) (1 + 6, 8 + 1) = (7, 9) = A’ B (−3, −5) (-3 + 6, -5 + 1) = (3, -4) = B’ C (−4, 7) (-4 + 6, 7 + 1) = (2, 8) = C’ D (−6, −2) (-6 + 6, -2 + 1) = (0, -1) = D’

Let us just plot the preimage and the image. The horizontal translations of curves that represent functions work a little differently when compared to the horizontal translations of points on the coordinate plane. Let us observe the example below. Here, the preimage is f(x) and the image is f(x + 2). Surprisingly, f(x) has moved left by 2 units (instead of right by 2 units) to give f(x + 2). Yes, this is the case with horizontal translations of functions. But this is not the case with vertical translations. Vertical translations work just like how they work with the translations of points on the coordinate plane.

### Rules of Translation of Functions

By the above observation, the rules for writing the translated functions can be summarized as follows:

Translation of Function When k > 0 When k < 0

Horizontal Translation f(x) becomes f(x + k)

Moves f(x) “k” units left. Moves f(x) “k” units right. Vertical Translation f(x) becomes f(x) + k Moves f(x) “k” units up Moves f(x) “k” units down

Here are some examples:

1. f(x – 2) + 3 moves f(x) by 2 units right and 3 units up.
2. g(x + 3) – 5 moves g(x) by 3 units left and 5 units down.

### Translating Graphs of Functions

To graph the translated graphs, we can move the given graph left/right/up/down using the above rules. Instead of this, we can translate a graph using the coordinates of some points on it. To graph a function translation f(x + k) + C when the graph of the function f(x) is given, just take some important points of the graph (where the shape is changing or taking turns) and find the new x and y coordinates of each point as follows.

• To find the new x-coordinate, set “x + k = old x-coordinate” and solve this for x.
• To find the new y-coordinate, use “old y-coordinate + C”.

After finding all the new points, just plot them and join them. This would give the translated graph. You can find an example of this process in the “Examples” section below.

The translation of any object can be represented by a column vector or column matrix as: (left(begin{array}{l} a \ \ b end{array}right)),

where a is the number of units to move right or left along the x-axis and b is the number of units to move up or down along the y-axis.

• The number at the top represents the right or left movement. A positive number means moving to the right and a negative number means moving to the left.
• The number at the bottom represents up and down movement. A positive number means moving up and a negative number means moving down.

In the following figure, triangle ABC is being translated to triangle A’B’C’: The translation from ABC to A’B’C’ is “2 units right and 3 units down” and the column vector that represents this translation is (left(begin{array}{c} 2 \ \ -3 end{array}right)).

Important Notes on Translations Math:

• While translating, all the points will shift by the same number of units.
• The shape or size of the object remains unaffected after translation.
• In the horizontal translation, the domain may be affected, whereas in the vertical translation, the range may be affected.

Related Topics:

• Types of Functions
• Cartesian Plane
• Coordinate Geometry

## Top 17 what is a translation in math edit by Top Q&A

### Translation – Math.net

• Author: math.net
• Published Date: 06/09/2022
• Review: 4.76 (534 vote)
• Summary: In geometry, a translation is a type of a transformation that moves a geometric figure in a given direction without changing the size or orientation of the …
• Matching search results: Here, the preimage is f(x) and the image is f(x + 2). Surprisingly, f(x) has moved left by 2 units (instead of right by 2 units) to give f(x + 2). Yes, this is the case with horizontal translations of functions. But this is not the case with …

### Translation | PBS LearningMedia

• Author: pbslearningmedia.org
• Published Date: 09/22/2022
• Review: 4.56 (260 vote)
• Summary: In this animated Math Shorts video from the Utah Education Network, learn about translation …
Dauer:
Gepostet:
• Matching search results: Here, the preimage is f(x) and the image is f(x + 2). Surprisingly, f(x) has moved left by 2 units (instead of right by 2 units) to give f(x + 2). Yes, this is the case with horizontal translations of functions. But this is not the case with …

### Translation Math

• Author: mathsux.org
• Published Date: 09/04/2022
• Review: 4.22 (519 vote)
• Summary: Translations are a type of transformation where we take a point, line, or shape and move it up, down, left, or right on a coordinate plane. A …
• Matching search results: The Game Plan: This question is asking us to find the translation from line RT to line R|T| . We’re going to need to compare corresponding coordinate points before and after the translation. We can look at a set of points before and after the …

### Translation | mathematics | Britannica

• Author: britannica.com
• Published Date: 03/24/2022
• Review: 4.06 (404 vote)
• Summary: …or a curve is called translation. Motion that changes the orientation of a body is called rotation. In both cases all points in the body have the same …
• Matching search results: The Game Plan: This question is asking us to find the translation from line RT to line R|T| . We’re going to need to compare corresponding coordinate points before and after the translation. We can look at a set of points before and after the …

### Translation – Transformations – GCSE Maths Revision – BBC Bitesize

• Author: bbc.co.uk
• Published Date: 12/23/2022
• Review: 3.86 (234 vote)
• Summary: A translation moves a shape up, down or from side to side but it does not change its appearance in any other way. Translation is an example of a transformation.
• Matching search results: The Game Plan: This question is asking us to find the translation from line RT to line R|T| . We’re going to need to compare corresponding coordinate points before and after the translation. We can look at a set of points before and after the …

Top 9 what time does planet fitnes close

### Reflection, Rotation, Translation | Turtle Diary Lesson

• Author: turtlediary.com
• Published Date: 04/28/2022
• Review: 3.73 (275 vote)
• Summary: There are three basic transformations that can be done to a shape:1. Reflection (flip) 2. Rotation (turn) 3. Translation (slide).
• Matching search results: The Game Plan: This question is asking us to find the translation from line RT to line R|T| . We’re going to need to compare corresponding coordinate points before and after the translation. We can look at a set of points before and after the …

### Translation Transformation (video lessons, examples and solutions) • Author: onlinemathlearning.com
• Published Date: 01/19/2022
• Review: 3.43 (457 vote)
• Summary: In a translation transformation all the points in the object are moved in a straight line in the same direction. The size, the shape and the orientation of the …
• Matching search results: The Game Plan: This question is asking us to find the translation from line RT to line R|T| . We’re going to need to compare corresponding coordinate points before and after the translation. We can look at a set of points before and after the …

### 8.9: Translation Notation – K12 LibreTexts

• Author: k12.libretexts.org
• Published Date: 05/20/2022
• Review: 3.25 (299 vote)
• Summary: Rules for Translations. Jack describes a translation as point moving from J(−2,6) to J′(4,9). Write the mapping rule to describe this …
• Matching search results: The Game Plan: This question is asking us to find the translation from line RT to line R|T| . We’re going to need to compare corresponding coordinate points before and after the translation. We can look at a set of points before and after the …

### What is translation of shapes?

• Author: theschoolrun.com
• Published Date: 05/16/2022
• Review: 3.19 (482 vote)
• Summary: In geometry translation means moving a shape into a different position, without changing it in any way. In Year 5 children are introduced to shape …
• Matching search results: The Game Plan: This question is asking us to find the translation from line RT to line R|T| . We’re going to need to compare corresponding coordinate points before and after the translation. We can look at a set of points before and after the …

Top 15 what is the purpose of a constitution

### Describing a Translation (KS3, Year 7)

• Author: mathematics-monster.com
• Published Date: 06/08/2022
• Review: 2.88 (96 vote)
• Summary: A translation moves a shape. Every point of the shape is moved in the same direction by the same distance. To describe a translation, we need to say in …
• Matching search results: The Game Plan: This question is asking us to find the translation from line RT to line R|T| . We’re going to need to compare corresponding coordinate points before and after the translation. We can look at a set of points before and after the …

### Translations – Varsity Tutors

• Author: varsitytutors.com
• Published Date: 03/23/2022
• Review: 2.76 (121 vote)
• Summary: A translation is a transformation that occurs when a figure is moved from one location to another location without changing its size, shape or orientation. In …
• Matching search results: The Game Plan: This question is asking us to find the translation from line RT to line R|T| . We’re going to need to compare corresponding coordinate points before and after the translation. We can look at a set of points before and after the …

### Translation – MathBitsNotebook(Geo – CCSS Math)

• Author: mathbitsnotebook.com
• Published Date: 04/30/2022
• Review: 2.67 (199 vote)
• Summary: A translation moves (“slides”) an object a fixed distance in a given direction without changing its size or shape, and without turning it or flipping it.
• Matching search results: The Game Plan: This question is asking us to find the translation from line RT to line R|T| . We’re going to need to compare corresponding coordinate points before and after the translation. We can look at a set of points before and after the …

### Translation in Geometry — Examples and Explanation

• Author: storyofmathematics.com
• Published Date: 02/22/2022
• Review: 2.62 (117 vote)
• Summary: Simply put, a translation in math is a vertical shift, horizontal shift, or a combination of the two. Examples. This section covers common examples of problems …
• Matching search results: As before, use the vertices of the square as the key points. We notice that A is at (1, 1), B is at (4, 1), C is at (4, 4), and D is at (1, 4). Since this is a movement downward, we will subtract 5 from the y-value of each vertex. This will give the …

Top 10+ what is a stock dividend

### Translation Definition (Illustrated Mathematics Dictionary) – Math is Fun

• Author: mathsisfun.com
• Published Date: 05/29/2022
• Review: 2.45 (175 vote)
• Summary: Illustrated definition of Translation: Sliding: moving a shape without rotating or flipping it. The shape still looks exactly the same, just in a…
• Matching search results: As before, use the vertices of the square as the key points. We notice that A is at (1, 1), B is at (4, 1), C is at (4, 4), and D is at (1, 4). Since this is a movement downward, we will subtract 5 from the y-value of each vertex. This will give the …

### What is a Translation? | Virtual Nerd

• Author: virtualnerd.com
• Published Date: 04/10/2022
• Review: 2.29 (165 vote)
• Summary: Real math help. … If so, then you have performed a translation! In this tutorial, learn the definition of translation and see some really neat examples.
• Matching search results: As before, use the vertices of the square as the key points. We notice that A is at (1, 1), B is at (4, 1), C is at (4, 4), and D is at (1, 4). Since this is a movement downward, we will subtract 5 from the y-value of each vertex. This will give the …

### Translations review (article) – Khan Academy

• Published Date: 09/20/2022
• Review: 2.39 (82 vote)
• Summary: 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 …
• Matching search results: As before, use the vertices of the square as the key points. We notice that A is at (1, 1), B is at (4, 1), C is at (4, 4), and D is at (1, 4). Since this is a movement downward, we will subtract 5 from the y-value of each vertex. This will give the …

### What is Translation in Math? – Definition, Examples, & Terms

• Author: study.com
• Published Date: 10/29/2022
• Review: 2.21 (99 vote)
• Summary: Translation is a term used in geometry to describe a function that moves an object a certain distance. The object is not altered in any other …
• Matching search results: As before, use the vertices of the square as the key points. We notice that A is at (1, 1), B is at (4, 1), C is at (4, 4), and D is at (1, 4). Since this is a movement downward, we will subtract 5 from the y-value of each vertex. This will give the …

### Related Posts ## Top 10+ what is a clo

Below is a list of the best what is a clo voted by users and compiled by us, invite you to learn together ## Top 20+ what trimester is 27 weeks

Here are the top best what trimester is 27 weeks public topics compiled and compiled by our team ## Top 10+ what fish is dory

Below are the best information about what fish is dory voted by users and compiled by us, invite you to learn together ## List of 10+ what is a burnt offering

Below are the best information about what is a burnt offering voted by readers and compiled and edited by our team, let’s find out