Explanation
To solve direction problems accurately, we track the person's movement step-by-step on a standard two-dimensional coordinate system layout where:
North is along the positive y-axis (+y).
South is along the negative y-axis (−y).
East is along the positive x-axis (+x).
West is along the negative x-axis (−x).
Let the initial starting position of the person be the origin point, P0=(0,0).
Step-by-Step Movement Tracking
Step 1: Moves 6 km towards North
Moving straight up along the North direction changes the vertical coordinate:
P1=(0, 0+6)=(0,6)
Step 2: Takes a right turn and goes 7 km
Turning right from North faces East (+x direction):
P2=(0+7, 6)=(7,6)
Step 3: Takes a right turn and goes 3 km
Turning right from East faces South (−y direction):
P3=(7, 6−3)=(7,3)
Step 4: Takes a right turn and goes 3 km
Turning right from South faces West (−x direction):
P4=(7−3, 3)=(4,3)
Step 5: Finally takes a right turn and goes 3 km
Turning right from West faces back towards North (+y direction):
P5=(4, 3+3)=(4,6)
Analyzing the Final Position relative to Starting Point
Our initial coordinate position P0 is (0,0).
Our final coordinate position P5 is (4,6).
Let us compare the final point coordinates to the original position:
The x-coordinate has increased (0→4), which means the person is positioned to the East.
The y-coordinate has increased (0→6), which means the person is positioned to the North.
Combining these two vector offsets, the final position point lies exactly in the North-East quadrant relative to the reference starting point.
Looking at the options provided:
(a) North
(b) South
(c) East
Since the precise positional direction is North-East and it is not explicitly listed among options (a), (b), or (c), it falls under the "none of these" category.
Final Answer
The correct option is (d) none (as the exact direction is North-East).
