Point U is 12 m to the South of Point T. Point V is 17 m to the southwest of…

2025

Point U is 12 m to the South of Point T. Point V is 17 m to the southwest of point U. Point W is 8 m to the north of point V and 20 m to the east of point X. UWV forms a right-angled triangle. Point Y is 17 m to the northeast of point X. Point Z is 8 m to the south of Point Y. XZY forms a right-angled triangle.

Point Y is in which direction with respect to point W?

  1. A.

    South East

  2. B.

    North

  3. C.

    South West

  4. D.

    North West

Show answer & explanation

Correct answer: D

Concept: When a diagonal movement (northeast, southwest, etc.) between two points is combined with a stated right-angled triangle and one perpendicular leg length, the remaining leg can be found with the Pythagorean theorem — here every triangle uses the 8-15-17 triple (8² + 15² = 17²). Once each point's position is written as an (East-West, North-South) offset from a common origin, the direction from one point to another follows from the sign of each offset: a single non-zero offset gives a pure cardinal direction (N/S/E/W), while two non-zero offsets give a compound direction (NE/NW/SE/SW).

Application:

  1. Take point X as the origin (0 m East-West, 0 m North-South).

  2. Triangle X-Z-Y is right-angled, with hypotenuse XY = 17 m (Y is northeast of X) and vertical leg ZY = 8 m (Z is south of Y). The horizontal leg is XZ = √(17² − 8²) = √225 = 15 m, so Z sits 15 m east of X, and Y sits 15 m east and 8 m north of X.

  3. W is given as 20 m east of X, lying on the same West-East line as X and Z.

  4. Triangle U-W-V is right-angled, with hypotenuse UV = 17 m (V is southwest of U) and vertical leg VW = 8 m (W is north of V). The horizontal leg is UW = √(17² − 8²) = 15 m, so U sits 15 m east of W — the only placement consistent with V being southwest (not southeast) of U.

  5. Comparing Y's position (15 m east, 8 m north of X) with W's position (20 m east of X, on the same West-East line as X): Y is (15 − 20) = 5 m west of W, and 8 m north of W.

  6. Both offsets are non-zero (5 m west and 8 m north), so the direction of Y with respect to W is the compound North-West direction.

Cross-check: The two right-angled triangles are mirror constructions of the same 8-15-17 triple on either side of the West-East line through X, Z, and W. The X-Z-Y triangle raises Y by 8 m above that line, while W itself lies on that line, so Y must be north of W regardless of the exact horizontal gap. Combined with the 5 m East-West offset already found between Y and W, this independently confirms a North-West relationship, not a purely North one.

Hence, the direction of Y with respect to point W is North-West.

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