Given the following directional relationships between points:

- $A \# (12) B$ means $A$ is $21 ext{ m}$ east of $B$
- $A * (03) B$ means $A$ is $30 ext{ m}$ north of $B$
- $A \% (24) B$ means $A$ is $42 ext{ m}$ west of $B$
- $A @ (52) B$ means $A$ is $25 ext{ m}$ south of $B$

And the conditions:

- $X \# (93) Y$
- $T * (42) U$
- $R @ (61) Q$
- $T \# (03) S$
- $P \% (14) Q$
- $W @ (61) X$
- $Z * (01) Y$
- $W \% (45) U$
- $S * (80) R$

**Question:** Which set of points lies on a straight line?

Question

Given the following directional relationships between points:

- $A \# (12) B$ means $A$ is $21 	ext{ m}$ east of $B$
- $A * (03) B$ means $A$ is $30 	ext{ m}$ north of $B$
- $A \% (24) B$ means $A$ is $42 	ext{ m}$ west of $B$
- $A @ (52) B$ means $A$ is $25 	ext{ m}$ south of $B$

And the conditions:

- $X \# (93) Y$
- $T * (42) U$
- $R @ (61) Q$
- $T \# (03) S$
- $P \% (14) Q$
- $W @ (61) X$
- $Z * (01) Y$
- $W \% (45) U$
- $S * (80) R$

**Question:** Which set of points lies on a straight line?

Accepted Answer

**Solution:**

1. First, interpret the symbols and distances:
   - $\#$ indicates east direction
   - $*$ indicates north direction
   - $\%$ indicates west direction
   - $@$ indicates south direction

2. Using the given conditions, plot the points step-by-step:
   - $X \# (93) Y$: $X$ is 21 m east of $Y$
   - $T * (42) U$: $T$ is 30 m north of $U$
   - $R @ (61) Q$: $R$ is 25 m south of $Q$
   - $T \# (03) S$: $T$ is 21 m east of $S$
   - $P \% (14) Q$: $P$ is 42 m west of $Q$
   - $W @ (61) X$: $W$ is 25 m south of $X$
   - $Z * (01) Y$: $Z$ is 30 m north of $Y$
   - $W \% (45) U$: $W$ is 42 m west of $U$
   - $S * (80) R$: $S$ is 30 m north of $R$

3. By carefully placing these points on a coordinate plane according to the directions and distances, we observe that points $Y$, $X$, and $R$ align perfectly in a straight line.

4. Other options do not satisfy the condition of collinearity based on the given directions and distances.

**Answer:** Y, X, R

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