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Translation in Math

In this page we are goimng to discuss about translation concept .Translation means moving a figure or a shape from one place to another. In translation a figure can move upward, downward, right, left or anywhere in the plane. It can change their path like At first it moves left then after it will take turn right then again right and so on. But If the one point of a shape (shape may be anything like Triangle, Rectangular, Square, Line, Circle etc) move five unit in forward direction then all the points will move by five unit in same direction. Suppose one point of a triangle move four unit in lift direction then all points of triangle move four unit in left direction. In translation only the positon of the object changes,its size remains the same.

 

Math Translation Examples

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Below are the examples on translation in Math :

Example 1:

An example of translation towards right is given below.

Math Translation

Here The figure "L" is shifted to right direction with a fix distance .The shape and size of the image is the same after the translation on position of image changes

Example 2:

An example of translation towards left is given below

Math Translation Examples

Here The figure is shifted in left direction 2`1/2` unit.Here also we can see that the shape and size remains the same only the position varies.

Example 3:

Math Translation Problems

Here ABCDE is a pentagon and translated pentagon A'B'C'D'E' it has sifted in left direction with a fix unit.All the points in the image is shifted to the new position.

Example 4:

Here is an example of translating an images in more than one direction.

Math Translation Figure

Here the rhombus is first moved x unit towards right direction and then moved y unit in upward direction.Thus the rhombus AB is shifted to new position A'B'

How to Solve Translation

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Below see the example to understand the concept of how to solve translation -

Problem 1:

A rectangular have on a graph with the points A(-5,7), B(2,7), C(-5,3), D(2,3) as shown in the figure. Shift it by five unit downward. Find the translated figure?

Math Translation Graph

Solution:

If the figure will translated by five unit in downward direction,

So, their is no change in x- coordinate or horizental direction

So , we have to subtract by -5 in y coordinate

So, we get

A(-5, 7) so, after translation coordinate will be (x-0, y-5)

(-5-0, 7-5)

(-5, 2) translated coordinate.

Now for B(2, 7) so, after translation coordinate will be (x-0, y-5)

(2-0, 7-5)

(2, 2) translated coordinate.

Now for C(-5, 3) so, after translation coordinate will be (x-0, y-5)

(-5-0, 3-5)

(-5, -2) translated coordinate.

Now for D(2, 3) so, after translation coordinate will be (x-0, y-5)

(2-0, 3-5)

(2, -2) translated coordinate.

so translated figure i

How to Solve Translation

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