Understanding Direction and Relative Positioning

This problem involves understanding directions and how they change relative to a person's facing direction. We are given Latika's facing direction and the waiter's position relative to Latika, described by an angle and direction from Latika's right side.

Analyzing Latika's Direction

We are told that Latika is facing West. The standard directions are North, South, East, and West. They are arranged such that North is opposite South, and East is opposite West. Moving 90 degrees clockwise from North takes you to East, from East to South, from South to West, and from West to North.

Determining Latika's Right Side

When a person is facing a certain direction, their right side points in a direction 90 degrees clockwise from their facing direction.

• If facing North, right is East.
• If facing East, right is South.
• If facing South, right is West.
• If facing West, right is North.

Since Latika is facing West, her right side is pointing North.

Locating the Waiter's Position

The waiter stands at 90° to the right of Latika. We just determined that Latika's right side is North. Standing at 90° to someone's right typically means standing beside them, towards their right side, but not necessarily facing the same direction. The phrase "90° to the right of Latika" here describes the *position* relative to Latika's right side. If Latika's right is North, then 90° to that direction is not the intended meaning. A more common interpretation in such puzzles is that the waiter is positioned in the direction that is 90° clockwise from Latika's facing direction, or simply positioned on her right side. Given the options, the most plausible interpretation is that the waiter is standing to Latika's North (her right side).

Let's consider the relative position:

• Latika faces West.
• Her right is North.
• The waiter stands "at 90° to the right of Latika". This means the waiter is located relative to Latika. The wording is slightly ambiguous but likely means the waiter is positioned in a way that makes sense in the context of a restaurant interaction. If the waiter is "to the right of Latika" while she faces West, the waiter is generally to her North. The "90°" might refer to the position being 90° from Latika's forward view towards her right.

So, the waiter is positioned to Latika's North.

Determining the Waiter's Facing Direction

The waiter is taking Latika's order. In a restaurant setting, the waiter usually faces the customer when taking their order. The waiter is standing to the North of Latika, who is facing West. For the waiter to face Latika from the North position, the waiter must be facing South.

Let's visualize this:

• Latika is at point L, facing West.
• Her right side is North.
• The waiter is at point W, located North of Latika.
• To take Latika's order (who is at L), the waiter (at W) must face towards L.
• The direction from W (North of L) towards L is South.

Therefore, the waiter is facing South.

Conclusion

Based on the interpretation that the waiter is positioned to Latika's right (North) and is facing her to take her order, the waiter is facing South.

Revision Table: Cardinal Directions and Relatives

Additional Information: Directional Reasoning Concepts

Directional reasoning questions test your understanding of cardinal directions (North, South, East, West) and ordinal directions (like North-East, South-West), as well as relative directions (left, right, front, back). These questions often involve imagining yourself or an object moving or positioned in space.

• Absolute Directions: These are the fixed points of the compass (North, South, East, West).
• Relative Directions: These are directions relative to a person or object's orientation (left, right, in front, behind). What is "right" depends on which way you are facing.
• Turns and Angles: Turns are often described in degrees (e.g., 90°, 180°, 270°) or as fractions of a turn (quarter turn, half turn). Clockwise is to the right, counter-clockwise is to the left. A 90° turn moves you to the next cardinal direction (e.g., North to East).
• Perspective: It's crucial to keep track of whose perspective you are considering (Latika's, the waiter's, or an external observer's). In this problem, the waiter's *position* is described relative to Latika, but the waiter's *facing direction* is inferred based on the context of the interaction.

Practicing visualizing these movements and positions can help solve such reasoning problems effectively.