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برنامه Mate Translate (با نام قبلی Instant Translate) این امکان را به شما می‌دهد تا کلمات خود را در بیش از ۱۰۰ زبان مختلف ترجمه کنید. می‌توانید از امکان text-to-speech برای خواندن لغت مورد نظر استفاده کنید و لغت‌ها را در history برنامه خود داشته. New: Main window hotkeys Ctrl+Alt+1.9 for opening dictionary with selected 1.9th service New: Main window hotkey Ctrl+Up to copy translation to the text input box New: Mouse mode 'Show translation and read'. English Translation of “mate” The official Collins Spanish-English Dictionary online. Over 100,000 English translations of Spanish words and phrases. UPDATE (v.2.0): Now you can highlight or right-click a text and translate it vs. Translate the entire page. You can also change extension options to automatically show translation every time you highlight text.

Related Pages
Transformations In Math
Geometric Transformations
Transformations In The Coordinate Plane
Rotation
More Geometry Lessons

What Is Translation?

In a translation transformation all the points in the object aremoved in a straight line in the same direction. The size, the shape and the orientation of theimage are the same as that of the original object. Same orientation means that the object and imageare facing the same direction.

Example:

We describe a translation in terms of the number of units moved to the right or left and thenumber of units moved up or down.

Example:
Move the object 2 units to the right and 4 units up.

Translation Represented By Column Vector Or Matrix

The translation can be represented by a column vector as.

The top number represents the right and left movement. A positive number means moving to the rightand a negative number means moving to the left.

The bottom number represents up and down movement. A positive number means moving up and anegative number means moving down.

In the following figure, triangle ABC is being translated to triangle A’B’C'

The translation is represented by the column vector.

In general, a translation can be represented by a column matrix or column vector wherea is the number of units to move right or left along the x-axis and b is the number of units tomove up or down along the y-axis.

The matrix equation representing a translation is:
where is the translation matrix and is the image of .

Example 1:
The triangle P is mapped onto the triangle Q by the translation .

a) Find the coordinates of triangle Q.
b) On the diagram, draw and label triangle Q.

Solution:
a)

b)

As a mathematical notation, we may write: T(A) = B, to mean object A is mapped onto B underthe transformation T.

Describing translations of simple shapes in the plane, using column vector notation

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How to transform a shape using a given vector?

Translation On The Coordinate Plane

Geometry Translation
A geometry translation is an isometric transformation, meaning that the original figure andthe image are congruent. Translating a figure can be thought of as “sliding” the original.If the image moved left and down, the rule will be (x - __, y - __) where the blanks are thedistances moved along each axis; for translations left and up: (x - __, y + __), for rightand down (x + __, y - __), for right and up (x + __, y + __).

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How to translate a polygon on the coordinate plane?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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