# 3D Reflection

The Reflection is a mirror image of the original object. We can differentiate 2D and 3D reflection by adding Z-axis. The Z-axis shows the depth of the surface. In the Reflection process, the size of the object does not change.

**We can represent Reflection by using the following three ways-**

**Reflection along with xy Plane:**In the xy plane reflection, the value of z is negative.

**x _{1} = x_{0}**

**y _{1} = y_{0}**

**z _{1} = **-

**z**

_{0}**Matrix of 3D Reflection-**

**Reflection along with xz Plane:**In the xz plane reflection the value of y is negative.

**x _{1} = x_{0}**

**y _{1} = -y_{0}**

**z _{1} = z_{0}**

**Matrix of 3D Reflection-**

**Reflection along with yz Plane:**In the yz plane reflection the value of x is negative.

**x _{1} = -x_{0} **

**y _{1} = y_{0}**

**z _{1} = z_{0}**

**Matrix of 3D Reflection-**

**Example: **A 3D triangle with coordinates points P (4, 5, 2), Q (7, 5, 3), R (6, 7, 4). Apply reflection on xy plane and find the new coordinates of triangle?

**Solution: **We have,

The initial coordinates of triangle = P (4, 5, 2), Q (7, 5, 3), R (6, 7, 4)

Reflection Plane = xy

Let the new coordinates of triangle = (x_{1}, y_{1}, z)

**For Coordinate P (4, 5, 2)**-

X_{1} = x_{0} = 4

y_{1} = y_{0} = 5

z_{1} = -z_{0}= -2

**The new coordinates = (4, 5, -2)**

**For Coordinate Q (7, 5, 3)**-

X_{1} = x_{0} = 7

Y_{1} = y_{0} = 5

Z_{1} = -z_{0}= -3

**The new coordinates = (7, 5, -3)**

**For Coordinate P (6, 7, 4)**-

X_{1} = x_{0} = 6

y_{1} = y_{0} = 7

z_{1} = -z_{0}= -4

**The new coordinates = (6, 7, 4)**