Solving Direction and Turn Reasoning Questions

Direction and turn questions test your spatial reasoning ability. To solve these problems, it's helpful to visualize the standard directions and understand how turns (clockwise and anticlockwise) affect the facing direction.

The standard directions are North, South, East, and West. The intercardinal directions are North-East, South-East, South-West, and North-West.

• An angle of $45^{\circ}$ separates a main direction from an adjacent intercardinal direction (e.g., North and North-East).
• An angle of $90^{\circ}$ separates two adjacent main directions (e.g., North and East) or two adjacent intercardinal directions (e.g., North-East and South-East).

Step-by-Step Analysis of Reeta's Turns

Let's track Reeta's facing direction after each turn starting from South-East.

Initial Direction: South-East

Turn 1: $135^{\circ}$ clockwise from South-East.

• From South-East, $45^{\circ}$ clockwise is South.
• From South, $90^{\circ}$ clockwise is West ($45^{\circ}$ to South-West, then $45^{\circ}$ to West).
• Total clockwise turn: $45^{\circ} + 90^{\circ} = 135^{\circ}$.
• After Turn 1, Reeta is facing West.

Turn 2: $90^{\circ}$ anticlockwise from West.

• From West, $90^{\circ}$ anticlockwise is South ($45^{\circ}$ to South-West, then $45^{\circ}$ to South).
• After Turn 2, Reeta is facing South.

Turn 3: $45^{\circ}$ clockwise from South.

• From South, $45^{\circ}$ clockwise is South-West.
• After Turn 3, Reeta is facing South-West.

Turn 4: $135^{\circ}$ anticlockwise from South-West.

• From South-West, $45^{\circ}$ anticlockwise is South.
• From South, $90^{\circ}$ anticlockwise is East ($45^{\circ}$ to South-East, then $45^{\circ}$ to East).
• Total anticlockwise turn: $45^{\circ} + 90^{\circ} = 135^{\circ}$.
• After Turn 4, Reeta is facing East.

Alternative Method: Calculating Net Displacement Angle

We can also find the final direction by calculating the net effect of all turns.

• Total clockwise turns: $135^{\circ} + 45^{\circ} = 180^{\circ}$ clockwise.
• Total anticlockwise turns: $90^{\circ} + 135^{\circ} = 225^{\circ}$ anticlockwise.

Net turn = Total Anticlockwise turns - Total Clockwise turns

Net turn = $225^{\circ}$ (Anticlockwise) - $180^{\circ}$ (Clockwise) = $45^{\circ}$ (Anticlockwise)

So, from her initial direction (South-East), Reeta makes a net turn of $45^{\circ}$ anticlockwise.

• Starting from South-East, a $45^{\circ}$ anticlockwise turn leads to East.

Both methods confirm that Reeta is finally facing East.

Summary of Turns

Final Direction

After completing all the turns, Reeta is facing East.

Revision Table: Key Concepts for Direction Problems

Additional Information on Direction Reasoning

Direction reasoning questions often involve sequences of turns or movements. It's crucial to correctly identify the starting direction and the type and magnitude of each turn. Visualizing the directions on a compass rose can be very helpful. Remember that a full circle is $360^{\circ}$. Turning $360^{\circ}$ clockwise or anticlockwise brings you back to the original direction. A $180^{\circ}$ turn results in facing the opposite direction.