# Translation in Math Worksheets, Definition, and Examples

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### Key Points about Translations in Math

• Translations in math are a fundamental concept that plays a crucial role in geometry.
• To translate a figure in math, you need to know the distance and the direction you want to move it.
• Math translation rules are straightforward and easy to understand.

## What is a Translation in Math?

Translations in Math involves sliding figures on a coordinate grid. Translation in Math takes place when a figure slides up/down or left/right. You can Translate in Math by changing the x and y coordinates. If you add to the y-coordinate, the figure will go up. If you subtract from the y-coordinate, the figure will go down. If you add to the x-coordinate, the figure will move right. If you subtract from the x-coordinate, the figure will move left. The last step for Translations in Math is to write the coordinates of the new location of the figure. If you are looking for the definition of Translation in Math keep scrolling down! Be sure to check out our translations maths worksheets on the left if you want more practice on Translation example problems or finding the definition for Translation in Math.

Translations in math are a fundamental concept that plays a crucial role in geometry. A translation is a transformation that moves an object from one location to another without changing its size, shape, or orientation. This concept is used in various fields, including computer graphics, engineering, and physics, making it a crucial topic for students to learn.

To translate a figure in math, you need to know the distance and the direction you want to move it. The direction can be horizontal, vertical, or diagonal, and the distance can be positive or negative. The distance and direction determine the new location of the figure. Translations are essential for understanding other transformations, such as rotations, reflections, and dilations, making it an important concept to master.

Math translation rules are straightforward and easy to understand. To translate a figure, you add or subtract a constant value to the x and y coordinates of each point in the figure. The translation formula is (x,y) → (x + a, y + b), where a is the horizontal distance and b is the vertical distance. By understanding these rules, students can quickly grasp the concept of translations and apply them to various problems.

Common Core Standard: 8.G.4
Related Topics: Congruent Shapes, Similar Figures, Rotation on a Coordinate Grid, Reflection on a Coordinate Grid, Dilation on a Coordinate Grid

## How to Translate in Math

Performing translations is a fundamental concept in geometry that involves moving an object to a new position without altering its shape, size, or orientation. In math, a translation is a transformation that shifts an object by a certain distance in a specific direction. This section will explain how to translate in math and provide examples to help you understand the concept better.

To perform a translation, you need to know the direction and distance you want to move the object. If you want to move an object to the right, you need to add a positive value to its x-coordinate. Similarly, if you want to move an object to the left, you need to subtract a negative value from its x-coordinate. To move an object up, you need to add a positive value to its y-coordinate, while to move it down, you need to subtract a negative value from its y-coordinate.

For example, suppose you have a point (2, 3) that you want to move to the right by 4 units and up by 2 units. To perform this translation, you need to add 4 to the x-coordinate and 2 to the y-coordinate. So, the new position of the point will be (6, 5).

In general, to translate an object in the x-direction, you add or subtract a value from its x-coordinate, and to translate it in the y-direction, you add or subtract a value from its y-coordinate. The table below summarizes the direction and distance of translations in math.

Directionx-coordinatey-coordinate
RightPositiveZero
LeftNegativeZero
UpZeroPositive
DownZeroNegative

Note that when an object is translated, its x- and y-coordinates are shifted by the same amount. Therefore, the distance between any two points on the object remains the same.

In conclusion, translating an object in math involves moving it a certain distance in a specific direction without changing its shape, size, or orientation. To perform a translation, you need to know the direction and distance you want to move the object and add or subtract the corresponding values from its x- and y-coordinates.

## Math Translation Rules

In mathematics, a translation is a type of transformation that moves a figure or object from one position to another without changing its shape, size or orientation. This section will discuss the rules for translating objects along the X-axis and Y-axis.

### Translation Along X-Axis

A translation along the X-axis moves an object horizontally. To translate a point or figure along the X-axis, we add or subtract a constant value to the x-coordinate of each point.

For example, consider the point P(2,3) translated 4 units to the right along the X-axis. The new point P’ can be found by adding 4 to the x-coordinate of P. Therefore, P’ is (6,3).

In general, if a point P(x,y) is translated a units to the right, the new point P'(x+a,y) is obtained. Similarly, if P is translated a units to the left, the new point P'(x-a,y) is obtained.

### Translation Along Y-Axis

A translation along the Y-axis moves an object vertically. To translate a point or figure along the Y-axis, we add or subtract a constant value to the y-coordinate of each point.

For example, consider the point Q(4,5) translated 3 units up along the Y-axis. The new point Q’ can be found by adding 3 to the y-coordinate of Q. Therefore, Q’ is (4,8).

In general, if a point Q(x,y) is translated b units up, the new point Q'(x,y+b) is obtained. Similarly, if Q is translated b units down, the new point Q'(x,y-b) is obtained.

In summary, translations in math move objects from one position to another without changing their size, shape, or orientation. To translate an object along the X-axis, we add or subtract a constant value to the x-coordinate of each point. To translate an object along the Y-axis, we add or subtract a constant value to the y-coordinate of each point.

## Translation in Math Definition

Translation is a geometric transformation that moves a figure in a given direction without changing its shape, size, or orientation. It is also known as a slide. In other words, translation is a function that maps each point of a figure to a new location, which is a certain distance and direction from the original point.

In mathematical terms, a translation is represented by a vector, which specifies the amount and direction of the movement. The vector is usually denoted by an arrow with its tail at the origin and its head at the new location of a point. The length and direction of the arrow represent the magnitude and direction of the translation, respectively.

Translations can be performed in any direction, including horizontal, vertical, and diagonal. They can also be combined with other transformations, such as rotations and reflections, to create more complex transformations.

Translations are used in many applications of mathematics, such as computer graphics, engineering, and physics. They are also a fundamental concept in Euclidean geometry, which studies the properties of figures in a plane or space.

In summary, a translation is a geometric transformation that moves a figure in a given direction without changing its shape, size, or orientation. It is represented by a vector that specifies the amount and direction of the movement. Translations are used in many fields of mathematics and are a fundamental concept in Euclidean geometry.

## 3 Simple Translation in Math Examples

Translation is a term used in geometry to describe a function that moves an object a certain distance without rotating, reflecting, or resizing it. In mathematical terms, a translation is a transformation that shifts every point of a figure or a graph by the same distance and in the same direction.

1. A translation math will slide a shape on the coordinate grid.
2. In order to slide a shape, you subtract or add to the coordinates of the figure.
3. Adding to the x value moves the figure right. Subtracting from the x value moves the figure left.
4. Adding to the y value moves the figure up. Subtracting from the y value moves the figure down.
5. Always redraw your figure on the coordinate grid when translating in math.

Here are a few examples of translation in math that can help students understand the concept better:

### Example 1: Translating a point on a coordinate plane

Suppose you have a point (3, 4) on a coordinate plane, and you want to translate it 2 units to the right and 3 units up. To do this, you can add 2 to the x-coordinate and 3 to the y-coordinate, which gives you the new point (5, 7). The table below shows the translation of the point (3, 4) to (5, 7):

Original PointTranslationNew Point
(3, 4)→ (2, 3)(5, 7)

### Example 2: Translating a triangle on a coordinate plane

Suppose you have a triangle with vertices at (1, 1), (2, 3), and (4, 2) on a coordinate plane, and you want to translate it 3 units to the right and 2 units up. To do this, you can add 3 to the x-coordinates and 2 to the y-coordinates of each vertex, which gives you the new triangle with vertices at (4, 3), (5, 5), and (7, 4). The table below shows the translation of the triangle:

Original TriangleTranslationNew Triangle
(1, 1), (2, 3), (4, 2)→ (3, 2)(4, 3), (5, 5), (7, 4)

### Example 3: Translating a function on a graph

Suppose you have a function f(x) = x^2 on a graph, and you want to translate it 2 units to the left. To do this, you can subtract 2 from the x-values of each point on the graph, which gives you the new function g(x) = (x + 2)^2. The figure below shows the translation of the function: These translation math examples demonstrate how to apply the concept of translation in different scenarios. By practicing more problems and questions, students can develop a better understanding of translation and its applications. Video lessons and study.com membership can also help students learn more about translation in math and other topics in mathematics.

## 5 Quick Translation in Math Practice Problems

/5

Translation in Math

Click Start to begin the practice quiz!

1 / 5

Translate the following point (x+6 , y-4)

(2 , 2)

2 / 5

Translate the following point right 3 and down 9.

(9 , 4)

3 / 5

Translate the following point left 8 and down 5.

(-5 , -2)

4 / 5

Translate the following point left 2 and up 4.

(-3 , 7)

5 / 5

Translate the following point (x-1 , y+3)

(5 , 2)

0%

## Translation in Math Formula

Translation is a type of transformation in mathematics that moves an object from one location to another without changing its size, shape, or orientation. It is commonly used in geometry to describe a function that moves an object a certain distance. The object is not altered in any other way. It is not rotated, reflected, or resized.

In mathematical notation, a translation is represented by the symbol “T” followed by a vector that describes the distance and direction of the movement. The vector is usually denoted by an ordered pair (a, b) or a column vector [a b]. The first component of the vector represents the horizontal distance, and the second component represents the vertical distance.

The translation rules for moving an object from one point to another are simple and straightforward. To translate an object, you need to add the horizontal and vertical distances to the corresponding coordinates of the object. For example, if you want to move a point (x, y) to a new location (x + a, y + b), you need to add the horizontal distance “a” to the x-coordinate and the vertical distance “b” to the y-coordinate.

Translation in math formula can also be expressed as a matrix multiplication. The translation matrix is a 3×3 matrix that has the following form:

``````| 1 0 a |
| 0 1 b |
| 0 0 1 |
``````

To translate an object using the matrix notation, you need to multiply the coordinates of the object by the translation matrix. For example, if you want to translate a point (x, y) by a distance of (a, b), you need to multiply the vector [x y 1] by the matrix:

``````| 1 0 a |
| 0 1 b |
| 0 0 1 |
``````

The result of the multiplication will be a new vector [x’ y’ 1] that represents the translated point. The new coordinates of the point are given by x’ = x + a and y’ = y + b.

In summary, translation in math formula is a simple and powerful tool that allows you to move objects from one location to another without changing their size, shape, or orientation. It can be expressed using mathematical notation, translation rules, or matrix multiplication. By understanding the basic principles of translation, you can solve a wide range of geometry problems and create stunning visual designs.

## Properties of Translations

Translations are a type of transformation that moves a shape left, right, up, or down without changing its size, orientation, or shape. A translation takes each point in a figure and slides it the same distance in the same direction. The properties of translations are essential in geometry, and they have significant implications in various fields, including computer graphics, engineering, and physics.

One of the fundamental properties of translations is that they preserve size and shape. When a figure undergoes a translation, it moves to a new location without being distorted in any way. As a result, the translated figure is congruent to the original figure, meaning they have the same shape and size. This property is crucial in geometry because it allows mathematicians to study figures without worrying about their orientation or position in space.

Another property of translations is that they preserve proportion. When a figure undergoes a translation, all distances in the figure are preserved. For example, if a line segment is translated, its length remains the same. Similarly, if two parallel lines are translated, they remain parallel after the translation. This property is vital in geometry because it allows mathematicians to study figures with respect to their relative positions and distances.

Furthermore, translations preserve distance. When a figure undergoes a translation, all points in the figure move the same distance in the same direction. As a result, the distance between any two points in the original figure is equal to the distance between the corresponding points in the translated figure. This property is crucial in geometry because it allows mathematicians to study figures with respect to their relative positions and distances.

In summary, translations are a type of transformation that moves a shape left, right, up, or down without changing its size, orientation, or shape. The properties of translations include preserving size, shape, proportion, and distance, which are essential in geometry.

## Math Translation FAQ

### What is a translation on a graph?

A translation on a graph is a type of transformation where a figure is moved from one location to another without changing its size, shape or orientation. It is also known as a slide. The figure is moved in a straight line, either vertically, horizontally, or diagonally. A translation can be represented on a graph by using coordinates.

### What are the 3 types of translations in math?

The three types of translations in math are horizontal, vertical, and diagonal translations. A horizontal translation moves the figure left or right, a vertical translation moves the figure up or down, and a diagonal translation moves the figure both vertically and horizontally.

### What is the rule for translations?

The rule for translations is to add or subtract a constant value to the x-coordinates and y-coordinates of the figure to move it to a new location. For example, to perform a horizontal translation of a figure by three units to the right, add 3 to the x-coordinates of all the points in the figure. Similarly, to perform a vertical translation of a figure by two units downwards, subtract 2 from the y-coordinates of all the points in the figure.

### How do you solve translations?

To solve translations, you need to know the rule for translating a figure and the coordinates of the original figure. Apply the rule to the coordinates of the original figure to find the coordinates of the new figure.

### How do you identify translations?

To identify translations, look for a figure that has been moved from its original position without changing its size, shape, or orientation. You can also look for a figure that has the same shape and size as the original figure but is located in a different position.

### How do you know if something is a translation in math?

You can know if something is a translation in math by looking for a figure that has been moved from its original position without changing its size, shape, or orientation. A translation is a type of transformation that moves a figure in a straight line, either vertically, horizontally, or diagonally.

### How do you explain translation?

Translation is a type of transformation in math where a figure is moved from one location to another without changing its size, shape or orientation. It is also known as a slide. A translation can be represented on a graph by using coordinates. To perform a translation, you need to know the rule for translating a figure and the coordinates of the original figure.

## Free Translation Worksheet: Video Explanation

Watch our free video on how to solve Translations. This video shows how to solve problems that are on our free Translation in Math worksheet that you can get by submitting your email above.

Watch the free Translation in Math video on YouTube here: Translation in Math

Video Transcript:
This video is about translations in math. You can get the worksheet we use in this video for free by clicking on the link in the description below. This video will help you answer the question what is translation in math?

Translation in math refers to when you take a shape or a point on the coordinate grid and you slide it on the coordinate grid. When translating in math your X and your Y coordinates control different ways to translate or slide. The X will control if the figure goes left or right and then the Y will control if it goes down or up.

For the figure to go left that means you’re going to subtract from the x coordinate, if it was going to go right you have to add to the x coordinate. For it to go down you’re going to subtract from the Y and then if it’s going to go up you will add to the Y.

If you are going to slide this shape, you can slide it right if you add to the X, you’ll slide it left if you subtract from the X, it’ll slide up if you add to the Y, and then it will slide down if you subtract from the Y. Most of the time it’ll be a combination of the change in the x and the y so you’ll go right and then up or left and then up or left and down. It just all depends on the problem.

The first problem on our translations in math worksheet says to translate figure ABCD 7 units right and 2 units up. We look at our figure ABCD and we know we have to translate seven units to the right and two units up. In order to do this we’re going to label each vertice and we’re going to count seven to the right and two up. Here we are at B, we’ll count one two three four five six seven and then up two and we’re going to label this B Prime.

And then we do the same thing for each coordinate. A up to this will be a prime and C goes seven to the right and then up to and then d, 7 to the right and then up to right there, D prime. Then we can connect our vertices and this will be our new shape.

Number two says translate figure ABCD X minus 5 and Y minus 10. We know that X controls if it’s going to go left or right and we know that Y controls if it goes up or down. If it’s X minus 5 that means we know it’s going to go left because anytime you subtract from the X it’s going to move left and because we’re subtracting 5 it’s going to go left 5. And then Y minus 10 that is also subtracting from Y so that means it’s going to go down 10 in the Y value.

Let’s go ahead and plot our vertices in red. We know it goes left 5  we’ll count 1 2 3 4 5 and then down 10 8 9 10. Now I’m going to label this a prime, and then we do that for each vertice. Once our new vertices are plotted we will connect the vertices to draw our new figure. And this will be the new figure after the translation math.