# 3D Translation

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A 3DTranslation 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 (x0, y0, z0) to Q (x1, y1, z1), then we have to add Translation coordinates (Tx, Ty, Tz) 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 (**Tx, Ty, Tz**) 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 = (x0, y0, z0) = (1,2,3)

Shift Vector = (Tx, Ty, Tz)

Let us assume the new coordinates of P = (x1, y1, z1)

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

X1 = x0 + Tx = (1 + 2) = 3

Y1 = y0 + Ty = (2 + 3) = 5

Z1 = z0 + Tz = (3 + 4) = 7

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