Q10. Direction: Study the information given below carefully and answer the…

2025

Q10. Direction: Study the information given below carefully and answer the question that follows. Point U is 12m to the South of Point T. Point V is 17m to the southwest of point U. Point W is 8m to the north of point V and 20m to the east of point X. UWV forms a right-angled triangle. Point Y is 17m to the northeast of point X. Point Z is 8m 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: This is a coordinate-based direction problem. Any two points connected by a stated straight-line distance and forming a right-angled triangle with one leg running due north-south and the other due east-west can be resolved using the Pythagorean theorem: for hypotenuse c with one known leg a, the other leg b = √(c² − a²). Once both points are placed as (east-west, north-south) offsets from a common origin, the direction of one point relative to another follows from the sign of the difference in each coordinate (positive east-west = East, negative = West; positive north-south = North, negative = South).

  1. Place X at the origin (0, 0). In right triangle XZY, the hypotenuse XY = 17m and the vertical leg YZ (Z lies south of Y) = 8m, so the horizontal leg XZ = √(17² − 8²) = √(289 − 64) = √225 = 15m.

  2. Because the right angle in triangle XZY is at Z, Z lies on the same east-west line as X. So the 8m vertical leg is Y's north offset from that line, and the 15m horizontal leg is Y's east offset from X. Y is therefore 15m east and 8m north of X.

  3. Point W is given as 20m east of X, with no north-south offset stated, so W sits on the same east-west line as X: W is 20m east and 0m north of X.

  4. Comparing Y (15m east, 8m north of X) with W (20m east, 0m north of X): Y's east offset (15m) is 5m short of W's (20m), so Y lies west of W; Y's north offset (8m) is positive relative to W's 0m, so Y also lies north of W. Combined, Y is to the north-west of W.

Cross-check: The leg values satisfy 8² + 15² = 64 + 225 = 289 = 17², confirming the triangle solution independently of the direction reading. The negative east-west difference (west) together with the positive north-south difference (north) both point to the same north-west quadrant, matching the answer.

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