Directions (38-40): Study the information carefully and answer the questions given below.

Rohit is standing at point A and wants to reach point E. He can only move in a straight line, but there are obstacles in his path. Rohit first moves 4 km towards the north and reaches point B. From there, he turns left and moves 3 km towards the west and reaches point C. He then turns left again and moves 5 km towards the south and reaches point D. Finally, he turns right and moves 8 km and reaches point E. Sonia wants to travel from point E to point A, but there is an additional obstacle in her path. There is a mountain between points E and A, which she cannot cross. Sonia first moves 5 km towards the south from point E and reaches point F. From there, she turns right and moves 6 km and reaches point G. She then turns left and moves 7 km towards the south and reaches point H. Finally, she turns right and moves 3 km and reaches point I. From point I, Sonia needs to reach point A, with shortest distance.

If Kavita is in north of point G and west of point A then in which direction is she with respect to point D?

To determine the direction of Kavita with respect to point D, let us represent the positions of all points on a Cartesian coordinate plane, taking point A as the origin (0, 0).

Step 1: Trace Rohit's path to locate points A, B, C, D, and E
1. Rohit starts at point A. Let

$A\; =\; (0,\; 0)$

2. He moves 4 km towards the north to reach point B. Since north is along the positive y-axis:

$B\; =\; (0,\; 4)$

3. From B, he turns left (west) and moves 3 km to reach point C. Since west is along the negative x-axis:

$C\; =\; (0\; -\; 3,\; 4)\; =\; (-3,\; 4)$

4. From C, he turns left again (facing west, a left turn points south) and moves 5 km to reach point D:

$D\; =\; (-3,\; 4\; -\; 5)\; =\; (-3,\; -1)$

5. From D, he turns right (facing south, a right turn points west) and moves 8 km to reach point E:

$E\; =\; (-3\; -\; 8,\; -1)\; =\; (-11,\; -1)$

Step 2: Trace Sonia's path from point E to locate points F and G
1. Sonia starts from point E (-11, -1) and moves 5 km towards the south to reach point F:

$F\; =\; (-11,\; -1\; -\; 5)\; =\; (-11,\; -6)$

2. From F, she turns right (facing south, a right turn points west) and moves 6 km to reach point G:

$G\; =\; (-11\; -\; 6,\; -6)\; =\; (-17,\; -6)$

Step 3: Find the position of Kavita
We are given two conditions for Kavita's position:
- Kavita is to the west of point A (0, 0). This means she lies on the same horizontal line as A (y-coordinate is 0) and is to the left of A (x-coordinate is negative).
- Kavita is to the north of point G (-17, -6). This means she lies on the same vertical line as G (x-coordinate is -17) and is above G (y-coordinate is greater than -6).
Combining these conditions, Kavita's coordinates must be:

$(-17,\; 0)$

Step 4: Determine Kavita's direction with respect to D
- D is located at (-3, -1).
- Kavita is located at (-17, 0).
Comparing the coordinates of Kavita with respect to D:
- Horizontal direction: Since -17 is less than -3, Kavita is to the West of D.
- Vertical direction: Since 0 is greater than -1, Kavita is to the North of D.
Therefore, Kavita is in the North-west direction with respect to point D.