# 3D Translation

A 3D Translation process contains the x-axis, y-axis, and z-axis. We can move any object from one place to another 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}, z

_{0}) to Q (x

_{1}, y

_{1}, z

_{1}), then we have to add Translation coordinates (T

_{x}, T

_{y}, T

_{z}) with original coordinates.

**We can also represent the 3D Translation in matrix form-**

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

- Line
- Rectangle
- Polygon
- Square

**3D Translation Matrix Representation:**

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

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

**Translation**or

**Shift Vector.**”

**Example:** A Point has coordinates P (1, 2, 3) in x, y, z-direction. Apply the translation with a distance of 2 towards x-axis, 3 towards y-axis, and 4 towards the z-axis. Find the new coordinates of the point?

**Solution:** We have,

Point P = (x_{0}, y_{0}, z_{0}) = (1,2,3)

Shift Vector = (T_{x}, T_{y}, T_{z})

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

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

X_{1} = x_{0} + T_{x} = (1 + 2) = 3

Y_{1} = y_{0} + T_{y} = (2 + 3) = 5

Z_{1} = z_{0} + T_{z} = (3 + 4) = 7

Thus, the new coordinates are = (3, 5, 7)