Direction sense and distance for SBI PO

Direction questions test one thing: can you keep track of where you are while reading a long sentence? Most wrong answers come from a single turn taken the wrong way halfway through, not from hard maths. The fix is to stop tracking in your head and write a coordinate after every move.

This guide sets out that method, the turn and rotation rules, the shadow rule, and the handful of right-angled triangles that SBI PO questions keep reusing.

How it is asked

• Walking questions: a person walks, turns and walks again. Where do they end up, how far from the start, and which way do they face?
• Point-to-point questions (common in the mains): "A is 5 m west of B. C is 6 m north of B…" Several points, several questions on the same set.
• Degree turns: "turns 135° anticlockwise".
• Shadow questions: morning or evening sun, and which way someone faces.
• Direction inside other topics: direction statements appear in data sufficiency and in some puzzles.

The coordinate method

Put the start at (0, 0). East is +x and north is +y. For each move:

When the walk ends at (x, y):

• Distance from the start = √(x² + y²).
• Direction from the start comes from the signs. +x and +y is north-east; +x and −y is south-east; −x and +y is north-west; −x and −y is south-west. If x = 0 or y = 0, it is due north, south, east or west.

In these questions "north-east" means anywhere in that quarter, not exactly 45°, unless the question says so.

Turns

Left and right depend on the way the person is facing, not on the page.

A right turn is 90° clockwise. A left turn is 90° anticlockwise.

Degree turns. Treat directions as bearings measured clockwise from north: N 0°, NE 45°, E 90°, SE 135°, S 180°, SW 225°, W 270°, NW 315°. Add for a clockwise turn, subtract for an anticlockwise turn, and take the result modulo 360.

Shadows

In the morning the sun is in the east, so shadows fall towards the west. In the evening the sun is in the west, so shadows fall towards the east. Work out where the shadow points, then use the turn table to find which way the person faces.

Triangles worth knowing

Most distance answers come from a few right-angled triangles. Spot them and skip the square root.

Worked examples

Example 1: a walk with turns. A person starts at P, walks 8 m north, turns right and walks 5 m, turns right and walks 14 m, then turns left and walks 3 m to reach T. Where is T from P?

• North 8: (0, 8), facing north.
• Right, so east 5: (5, 8).
• Right from east is south; 14 m: (5, −6).
• Left from south is east; 3 m: (8, −6).
• Distance √(64 + 36) = √100 = 10. Signs +x and −y.
• T is 10 m south-east of P.

Example 2: point to point (mains style). A is 5 m west of B. C is 6 m north of B. D is 8 m east of C. E is 6 m south of D.

Put B at (0, 0). Then A (−5, 0), C (0, 6), D (8, 6), E (8, 0).

1. Where is D from B? (8, 6): √(64 + 36) = 10 m north-east.
2. Where is E from A? Both lie on the line y = 0, 13 m apart: 13 m east.
3. Where is C from E? C − E = (−8, 6): 10 m north-west.

Example 3: final facing direction. A person walks 10 m south, turns left and walks 15 m, turns left and walks 10 m, then turns right and walks 5 m. Which way do they face, and where are they from the start?

• South 10: (0, −10). Left from south is east; 15 m: (15, −10).
• Left from east is north; 10 m: (15, 0). Right from north is east; 5 m: (20, 0).
• They face east and are 20 m east of the start.

Example 4: degree turns. A person faces north, turns 90° clockwise and then 135° anticlockwise. Which way do they face now?

• Start at 0°. Clockwise 90° gives 90° (east).
• Anticlockwise 135°: 90 − 135 = −45, which is 315°.
• North-west.

Example 5: shadow. One morning, a person stands so that their shadow falls exactly to their right. Which way do they face?

• Morning shadows point west, so west is on the person's right.
• From the turn table, a person facing south has west on their right.
• They face south.

Practice set

1. A person walks 15 m east, turns left and walks 8 m. How far and in which direction are they from the start?
2. From P, a person walks 6 m south, turns left and walks 10 m, then turns left and walks 6 m. Where are they from P, and which way do they face?
3. X is 5 m north of Y. Z is 12 m east of Y. What is the distance between X and Z?
4. A person faces south-east and turns 225° clockwise. Which way do they face?
5. In the evening, a person's shadow falls directly behind them. Which way do they face?
6. A person walks 9 m west, turns right and walks 5 m, turns right and walks 21 m, then turns right and walks 10 m. How far and in which direction are they from the start?
7. M is 6 m south of N. O is 8 m west of M. P is 6 m north of O. Where is P from N, and how far is O from N?

Answers:

1. 17 m north-east. The end point is (15, 8), and √(225 + 64) = √289 = 17.
2. 10 m east of P, facing north. (0, −6), then east to (10, −6), then north to (10, 0).
3. 13 m. A right angle at Y with sides 5 and 12.
4. North. South-east is 135°. Adding 225° gives 360°, which is 0°.
5. West. The evening sun is in the west and shadows fall east. The shadow is behind them, so they face west, towards the sun.
6. 13 m south-east. (−9, 0), then north to (−9, 5), then east to (12, 5), then south to (12, −5). √(144 + 25) = 13.
7. P is 8 m west of N; O is 10 m from N, to the south-west. With N at (0, 0): M (0, −6), O (−8, −6), P (−8, 0).

What to do next

• Solve ten walking questions writing a coordinate after every single move, even the easy ones.
• Learn the triangle table and the bearings (N 0°, E 90°, S 180°, W 270°).
• Do one point-to-point set a day for a week. Place every point on a single grid before answering.
• Direction statements reappear in data sufficiency in reasoning. For facing directions in seating, see linear seating.