# 2D Translation

We can move any object from one to another place without changing the shape of the object.

**For Example-**

**Translation of a Point:**If we want to translate a point from P (x_{0}, y_{0}) to Q (x_{1}, y_{1}), then we have to add Translation coordinates (Tx, Ty) with original coordinates.

**We can also represent the translation in matrix form-**

We can apply Translation on following object**s-**

**Line****Rectangle****Polygon****Square**

## Homogeneous Coordinate Representation:

The above Translation is also shown in the form of 3 x 3 matrix-

Here, Translation coordinates (**T _{x}, T_{y}**) are also called “

**Translation**or

**Shift Vector.**”

**Ex****ample**- Given a Point with coordinates (2, 4). Apply the translation with distance 4 towards x-axis and 2 towards the y-axis. Find the new coordinates without changing the radius?

**Solution: **P = (x_{0}, y_{0}) = (2,4)

Shift Vector = (T_{x}, _{Ty}) = (4, 2)

Let us assume the new coordinates of P = (x_{1}, y_{1})

Now we are going to add translation vector and given coordinates, then

x_{1} = x_{0} + T_{x} = (2 + 4) = 6

y_{1} = y_{0} + T_{y} = (4 + 2) = 6

Thus, the new coordinates = (6,6)