find the reflection of P(x,y,z) in the
(i) XY plane
(ii) YZ plane
(iii) ZX plane

Answer

To find the reflection of the point \( P(x, y, z) \) in the three coordinate planes (XY plane, YZ plane, and ZX plane), we can follow these steps:

### Step 1: Reflection in the XY Plane
- The XY plane is defined by \( z = 0 \).
- To find the reflection of point \( P(x, y, z) \) in the XY plane, we keep the x and y coordinates the same, but we change the sign of the z coordinate.
- Therefore, the reflection of point \( P \) in the XY plane is given by:
\[ P' = (x, y, -z) \]

### Step 2: Reflection in the YZ Plane
- The YZ plane is defined by \( x = 0 \).
- To find the reflection of point \( P(x, y, z) \) in the YZ plane, we keep the y and z coordinates the same, but we change the sign of the x coordinate.
- Therefore, the reflection of point \( P \) in the YZ plane is given by:
\[ P'' = (-x, y, z) \]

### Step 3: Reflection in the ZX Plane
- The ZX plane is defined by \( y = 0 \).
- To find the reflection of point \( P(x, y, z) \) in the ZX plane, we keep the x and z coordinates the same, but we change the sign of the y coordinate.
- Therefore, the reflection of point \( P \) in the ZX plane is given by:
\[ P''' = (x, -y, z) \]

### Summary of Reflections
- Reflection in XY plane: \( P' = (x, y, -z) \)
- Reflection in YZ plane: \( P'' = (-x, y, z) \)
- Reflection in ZX plane: \( P''' = (x, -y, z) \)