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?

The correct option is North-west.

Let us trace the coordinates of all the points by setting the starting point of Rohit, point A, as the origin $(0,0)$ on a standard Cartesian coordinate system where:
- East represents the positive x-direction.
- West represents the negative x-direction.
- North represents the positive y-direction.
- South represents the negative y-direction.

Step 1: Determine the positions of points A, B, C, D, and E
- Point A: Rohit starts at point A. Let its coordinates be:
$A=(0,0)$
- Point B: Rohit moves 4 km towards the north to reach point B:
$B=(0,0+4)=(0,4)$
- Point C: From B, he turns left (west) and moves 3 km to reach point C:
$C=(0-3,4)=(-3,4)$
- Point D: From C, he turns left (south) and moves 5 km to reach point D:
$D=(-3,4-5)=(-3,-1)$
- Point E: From D, he turns right (since he is facing south, a right turn is towards the west) and moves 8 km to reach point E:
$E=(-3-8,-1)=(-11,-1)$

Step 2: Determine the positions of points F, G, H, and I (Sonia's path)
- Point F: Sonia moves 5 km towards the south from point E:
$F=(-11,-1-5)=(-11,-6)$
- Point G: From F, she turns right (since she is facing south, a right turn is towards the west) and moves 6 km to reach point G:
$G=(-11-6,-6)=(-17,-6)$

Step 3: Find the position of Kavita
Let Kavita's coordinates be $(x,y)$.
- We are given that Kavita is to the north of point G. Since $G=(-17,-6)$, her x-coordinate must be equal to G's x-coordinate:
$x=-17$
- We are also given that Kavita is to the west of point A. Since $A=(0,0)$, her y-coordinate must be equal to A's y-coordinate:
$y=0$
Therefore, Kavita's coordinates are:
$\mathrm{Kavita}=(-17,0)$

Step 4: Find Kavita's direction with respect to point D
We compare Kavita's position $(-17,0)$ with respect to point D $(-3,-1)$:
- Comparing x-coordinates: $-17<-3$, which means Kavita is to the west of point D.
- Comparing y-coordinates: $0>-1$, which means Kavita is to the north of point D.
Combining these two components, Kavita is in the North-west direction with respect to point D.