Your house is located at X and your school is located at Y. Although your school is just opposite but you cannot go straight because of the busy highway in between. So, you first go 125 m due south, then cross a 100 m long subway which is due east and finally reach your school at Y which is 125 m due north. With respect to school at Y your house at X is

The correct answer is 100 m due west.

Step-by-step Explanation:

Step 1: Determine the position of the school at Y relative to your house at X
Let us consider the house at point X as the origin position (0, 0) on a standard 2D directional map, where North is upwards (+y), South is downwards (-y), East is to the right (+x), and West is to the left (-x).

1. First, you move 125 m due south from X:
Position after moving south = (0, -125 m)

2. Next, you cross a 100 m long subway due east:
Position after moving east = (+100 m, -125 m)

3. Finally, you move 125 m due north to reach your school at Y:
Position of Y = (+100 m, -125 m + 125 m) = (+100 m, 0)

Thus, school Y is located 100 m due East from house X.

Step 2: Determine the position of your house at X with respect to school at Y
The question asks for the position of house X with respect to school Y (taking Y as the reference point).

Since school Y is 100 m to the East of house X, house X must be located 100 m to the West of school Y.

Therefore, with respect to school Y, house X is 100 m due west.