Q.9
X is 1 km northeast of Y. Y is 1 km southeast of Z. W is 1 km west of Z.
P is 1 km south of W. Q is 1 km east of P.
What is the distance between X and Q in km?
- (A) 1
- (B) √2
- (C) √3
- (D) 2
Distance Between X and Q: 1 km Northeast Puzzle Solved (√3 km)
Northeast-southeast directional puzzles test coordinate mapping skills, with the correct distance between X and Q being √3 km.[web:1][web:3]
Problem Breakdown
Assign coordinates starting with Z at (0,0) for simplicity. Y lies 1 km southeast of Z, so at (√2/2, –√2/2). X is 1 km northeast of Y, positioning it at (√2, 0).[web:1]
W sits 1 km west of Z at (-1, 0), P 1 km south of W at (-1, -1), and Q 1 km east of P at (0, -1).[web:1][web:3]
Distance Calculation
Apply the distance formula √((x₂ – x₁)² + (y₂ – y₁)²) between X (√2, 0) and Q (0, -1):
√((0 – √2)² + (-1 – 0)²) = √(2 + 1) = √3
This confirms √3 km.[web:1]
Coordinates Table
| Point | Coordinates (x, y) |
|---|---|
| Z | (0, 0)[web:1] |
| Y | (√2/2, –√2/2)[web:1] |
| X | (√2, 0)[web:1] |
| W | (-1, 0)[web:1] |
| P | (-1, -1)[web:1] |
| Q | (0, -1)[web:1] |
Options Analysis
- (A) 1: Matches straight north-south or east-west separations, but X-Q involves diagonal offset.[web:1]
- (B) √2: Arises from single 45° moves (e.g., Z to Y), not the full X-Q vector.[web:1][web:3]
- (C) √3: Correct, from Δx = √2, Δy = 1.[web:1][web:3]
- (D) 2: Overestimates; straight-line is shorter than path sum.[web:1]
