The best way to think of this is to start with a rectangular box with base dimensions 5 by 1 and height 2 units.
The box has 8 corners and 6 sides or faces. The dimensions of the top are the same as the base, but the top is 2 units above the base.
Now imagine one corner of a rectangular room which has a floor joined to two vertical walls. We're going to place the box in this corner of the room so that its base rests on the floor and two of its faces are pressing against the walls.
Let's call the corner of the room the origin represented by the coordinates (0,0,0). One of the two walls is a mirror and this is the wall against which the long side of the box (5 by 2) has been placed. The other side (1 by 2) is against a blank, non-reflective wall.
All the corners of the box except one will be touching a wall or the floor. If we label this exceptional corner of the box P, then we can give its coordinate position as (5,1,2) because it's 2 units above the floor, 1 unit away from the mirror wall and 5 units away from the blank wall.
Now look at the reflection of P in the mirror. Call this reflection Q. It's 1 unit away from the wall, but it appears to be behind the wall in a mirror world. Q is still 5 units away from the blank wall and 2 units above the floor. We could say that the coordinates of Q are (5,-1,2).
If we call the vertical direction the z-axis, the bottom edge of the blank wall the y-axis and the bottom edge of the mirror wall the x-axis then, for Q, x=5, y=-1 and z=2, hence the coordinates of P are (5,1,2) and its reflection Q(5,-1,2).
You can view this picture in 3D by wearing filtered glasses---green or blue for right eye and red for left eye.
The box is labelled ABCDEFPG and its reflection (dotted edges) ABHIEFQJ. Q(5,-1,2) is the reflection of P(5,1,2).
