Understanding Directional Relationships and Distances

This question involves analyzing coded directional relationships and distances between different points to find the shortest distance between two specific points, G and C.

Let's first understand the meaning of each symbol provided:

• P$Q: P is to the north of Q.
• P&Q: P is to the east of Q.
• P*Q: Q is to the west of P (equivalent to P is to the east of Q).
• P%Q: Q is to the south of P (equivalent to P is to the north of Q).
• P@QR: P stands exactly in the middle of horizontal line QR.
• P!QR: P stands exactly in the middle of vertical line QR.

Note that distance is included, e.g., 'P6m$Q' means 'P is 6 m to the north of Q'.

Breaking Down the Expression: C12m$S5m*G3m&J6m%K!JT

We will analyze the given expression part by part:

1. C12m$S: C is 12m to the North of S.
2. S5m*G: G is 5m to the West of S.
3. G3m&J: G is 3m to the East of J.
4. J6m%K: J is 6m to the North of K.
5. K!JT: K is exactly in the middle of the vertical line JT.

Determining Relative Positions and Coordinates

Let's establish a coordinate system to represent the positions of the points. We can place S at the origin (0, 0) for simplicity.

• C12m$S: C is 12m North of S. If S is at (0, 0), C is at (0, 12).
• S5m*G: G is 5m West of S. If S is at (0, 0), G is at (-5, 0).
• G3m&J: G is 3m East of J. This means J is 3m West of G. Since G is at (-5, 0), J is at (-5 - 3, 0) = (-8, 0).
• J6m%K: J is 6m North of K. This means K is 6m South of J. Since J is at (-8, 0), K is at (-8, 0 - 6) = (-8, -6).
• K!JT: K is the midpoint of the vertical line JT. We know J is at (-8, 0) and K is at (-8, -6). Since K is the midpoint of JT and the line is vertical, T must be directly below K at the same horizontal position (-8). The distance JK is the difference in y-coordinates: $|0 - (-6)| = 6$m. Since K is the midpoint, the distance KT must also be 6m. T's y-coordinate will be K's y-coordinate minus 6. T is at (-8, -6 - 6) = (-8, -12).

Let's list the coordinates of the relevant points:

Calculating the Shortest Distance between G and C

We need to find the shortest distance between G and C. G is at (-5, 0) and C is at (0, 12). The shortest distance between two points in a coordinate plane is the straight line distance, which can be found using the Pythagorean theorem.

The difference in x-coordinates ($\Delta x$) is $|0 - (-5)| = 5$ m.

The difference in y-coordinates ($\Delta y$) is $|12 - 0| = 12$ m.

The shortest distance $d$ is given by the formula:

$$d = \sqrt{(\Delta x)^2 + (\Delta y)^2}$$

Substituting the values:

$$d = \sqrt{(5)^2 + (12)^2}$$

$$d = \sqrt{25 + 144}$$

$$d = \sqrt{169}$$

$$d = 13$$

The shortest distance between G and C is 13 m.

Final Answer

The shortest distance between G and C is 13 m.

Revision Table: Key Points

Additional Information: Solving Directional Distance Puzzles

Directional distance reasoning questions test your ability to understand and apply directions and distances to determine relative positions. Here are some tips for solving such problems:

• Carefully read and understand the meaning of each symbol and notation used in the problem.
• Break down the given expression or statements into smaller, manageable parts.
• Visualize the movements and positions. Drawing a diagram or using a coordinate system can be extremely helpful.
• Pay attention to keywords like "North," "South," "East," "West," and "middle" or "midpoint."
• For shortest distance calculations between two points that are not on the same horizontal or vertical line, the Pythagorean theorem is typically used. Identify the horizontal and vertical differences between the two points.
• Ensure you calculate the distance between the correct points as asked in the question.

Practicing various types of directional distance problems will improve your speed and accuracy in solving them.