Direction: Read the following information carefully and answer the questions…

Concept

In a direction-and-distance coding puzzle, every relation gives a displacement on a 2-D plane: the symbol fixes the direction (# = East, $ = North, % = West, @ = South) and the bracketed two-digit number is REVERSED to give the distance in metres. Fix one point as the origin (0, 0), plot each point by its displacement, and three points lie on a straight line exactly when they share one coordinate (same x = a vertical line, same y = a horizontal line) i.e. the signed area of the triangle they form is zero.

Application

Take Y = (0, 0) and build every point from the conditions (each number reversed):

1. X # (93) Y: X is 39 m East of Y → X = (39, 0).

2. W @ (61) X: W is 16 m South of X → W = (39, −16).

3. W % (45) U: W is 54 m West of U → U = (93, −16).

4. T $ (42) U: T is 24 m North of U → T = (93, 8).

5. T # (03) S: T is 30 m East of S → S = (63, 8).

6. S $ (80) R: S is 8 m North of R → R = (63, 0).

7. R @ (61) Q: R is 16 m South of Q → Q = (63, 16).

8. P % (14) Q: P is 41 m West of Q → P = (22, 16).

9. Z $ (01) Y: Z is 10 m North of Y → Z = (0, 10).

Final coordinates:

Cross-check

Scan for a shared coordinate. Y = (0, 0), X = (39, 0) and R = (63, 0) all have y = 0, so they sit on the same horizontal line (the x-axis) — these three are collinear.

• (63, 8), (63, 0), (93, −16): the first two share x = 63 but the third has x = 93, so they bend off — not a straight line.

• (63, 16), (63, 0), (39, −16): the first two share x = 63 but the third has x = 39, so the line breaks — not straight.

• (0, 0), (22, 16), (63, 16): the last two share y = 16 but the first has y = 0, so they are not aligned.

Only Y = (0, 0), X = (39, 0), R = (63, 0) lie on one straight line.