Direction sense: Reasoning Ability Notes for Maharashtra TET (Teacher Eligibility)

Direction Sense – Study Notes

(Maharashtra TET – Reasoning Ability)

1. Simple Explanation

Direction sense is the ability to identify the relative position of objects or points in space (e.g., north, south, east, west, left, right, above, below).
It is used in:

Compass‑based problems (N, S, E, W, NE, etc.)
Grid‑based mental‑rotation problems
Relative positioning on a plane or in three dimensions

In TET questions you will often be asked to determine the direction of one person/point relative to another after a series of movements.

2. Key Points

#	Concept	How to Apply	Common Pitfall
1	Basic cardinal directions	North = up, South = down, East = right, West = left (on a standard map).	Ignoring the 8‑point compass (NE, SE, SW, NW).
2	Relative direction	If A is north of B, then B is south of A.	Mixing up “from” vs “to”.
3	Left/Right in body‑centric terms	Facing a direction, left is counter‑clockwise, right is clockwise.	Assuming left/right is always from a fixed viewpoint (e.g., always left of the map).
4	Forward/Backward	Moving forward keeps the same direction; backward reverses it.	Forgetting that “backward” changes relative orientation.
5	Turning	90° turn = one cardinal direction change (N→E, E→S, etc.). 180° turn = opposite direction.	Over‑turning (e.g., a 270° turn is the same as a 90° turn to the opposite side).
6	Multi‑step sequences	Keep a mental or written record of each step; update the direction after each move.	Losing track of intermediate directions.
7	Grid & coordinates	Use (x, y) coordinates: +x = east, +y = north.	Mixing up positive/negative axes.
8	3‑D direction	Above, below, in front of, behind are relative to the observer’s orientation.	Assuming vertical directions are always the same regardless of orientation.

3. Worked Example

Problem

Five persons – A, B, C, D, E – stand in a straight line facing north.

A turns 90° to his right.

B turns 180° and then walks 2 steps forward.

C turns 90° to his left and walks 1 step forward.

D turns 270° to his right and walks 3 steps forward.

E turns 90° to his left and walks 1 step forward.

Question: If the line is drawn on a coordinate grid with the origin (0,0) at A’s initial position and the positive y‑axis pointing north, where is each person relative to A’s final position?

Solution

Step	Person	Initial direction (facing)	Turn	New direction	Forward steps	Final displacement (x, y)
1	A	North	90° right	East	0	(0,0)
2	B	North	180°	South	2	(0,-2)
3	C	North	90° left	West	1	(-1,0)
4	D	North	270° right = 90° left	West	3	(-3,0)
5	E	North	90° left	West	1	(-1,0)

Relative to A’s final position (0,0):

B is 2 units south (0, –2).

C is 1 unit west (–1, 0).

D is 3 units west (–3, 0).

E is 1 unit west (–1, 0).

Answer:
A is at the origin.
B is south of A.
C, D, and E are west of A (C and E same spot, D further west).

4. Quick Revision Summary

Topic	What to Remember
Cardinal points	N=up, S=down, E=right, W=left; NE=up‑right, etc.
Left/Right	Counter‑clockwise = left, clockwise = right (when facing current direction).
Turning	90° step = next cardinal; 180° = opposite; 270° = 90° the other way.
Forward/Backward	Forward keeps direction, backward reverses.
Relative direction	“X is north of Y” → Y is south of X.
Grid method	+x east, +y north. Use displacement vectors to track movement.
Common traps	Mixing up viewpoint, forgetting to update direction after each turn, overlooking 3‑D verticals.

Quick Practice Question

Q: If X is standing facing east and turns 90° left, then walks 3 steps forward, where is X relative to his starting point?

Answer:

After a 90° left turn from east, X faces north.
3 steps north → displacement (0, +3).
X is 3 units north of his starting point.

Use these guidelines to decode any direction‑sense question in the Maharashtra TET Reasoning section. Good luck!