Directions: Study the given information carefully and answer the question that follows.

Maya starts moving from point A towards the west for 11m to reach point B. Then, she turns right and walks for 4m to reach point C. Then she again turns right and walks for 14m to reach point D and then finally she turns towards south and walks for 6m to reach point E.

Neil starts walking towards north for 2m from point A to reach point F. Then, he takes a right turn and a left turn, walking for 6m and 9m to reach points G and H respectively. Then, he takes a left turn and walks for 5m to reach point I.

In which direction is point E with respect to point I?

The correct answer is South-east.

To determine the direction of point E with respect to point I, let us trace the movement of both Maya and Neil step-by-step using Cartesian coordinates, taking point A as the origin point (0, 0).

Let East represent the positive x-axis, West represent the negative x-axis, North represent the positive y-axis, and South represent the negative y-axis.

Maya's Path:

1. Maya starts from point A:

$\text{A}=(0,0)$

2. She moves west for 11 m to reach point B:

$\text{B}=(0-11,0)=(-11,0)$

3. She turns right (facing North) and walks 4 m to reach point C:

$\text{C}=(-11,0+4)=(-11,4)$

4. She turns right again (facing East) and walks 14 m to reach point D:

$\text{D}=(-11+14,4)=(3,4)$

5. Finally, she turns south and walks 6 m to reach point E:

$\text{E}=(3,4-6)=(3,-2)$

Neil's Path:

1. Neil starts from point A and walks north for 2 m to reach point F:

$\text{F}=(0,0+2)=(0,2)$

2. He turns right (facing East) and walks 6 m to reach point G:

$\text{G}=(0+6,2)=(6,2)$

3. He turns left (facing North) and walks 9 m to reach point H:

$\text{H}=(6,2+9)=(6,11)$

4. He turns left (facing West) and walks 5 m to reach point I:

$\text{I}=(6-5,11)=(1,11)$

Relative Position of Point E with respect to Point I:

Position of Point E: $(3,-2)$

Position of Point I: $(1,11)$

Horizontal displacement from I to E:

${\text{Δx}}_{}=3-1=+2\text{ (East)}$

Vertical displacement from I to E:

${\text{Δy}}_{}=-2-11=-13\text{ (South)}$

Since the displacement in the x-direction is positive (East) and the displacement in the y-direction is negative (South), point E is located in the South-east direction with respect to point I.