X walked 15 m south, turned left 15 m and turned left and walked for 15 m. How far and in which direction is he form the starting position?
15 m east
Understanding Direction and Distance Reasoning
Direction and distance reasoning questions involve tracing a path based on movement and turns. We need to determine the final position relative to the starting point, including both the distance and the direction.
Step-by-Step Path Analysis
Let's break down the movements of X:
- Starting Point: Assume X starts at the origin (0,0).
- Movement 1: X walked 15 m south. If we consider South along the negative y-axis, X's position is now (0, -15).
- Turn 1 & Movement 2: X turned left. From South, a left turn is towards the East (positive x-axis). X then walked 15 m in this direction. X's position is now $(0 + 15, -15) = (15, -15)$.
- Turn 2 & Movement 3: X turned left again. From East, a left turn is towards the North (positive y-axis). X then walked for 15 m in this direction. X's position is now $(15, -15 + 15) = (15, 0)$.
Determining Final Position Relative to Start
X started at (0,0) and ended at (15,0). We need to find the distance and direction of the final position (15,0) from the starting position (0,0).
Calculating the Distance
The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula: $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$.
Using the start point $(0,0)$ and end point $(15,0)$:
Distance $= \sqrt{(15-0)^2 + (0-0)^2}$
Distance $= \sqrt{15^2 + 0^2}$
Distance $= \sqrt{225}$
Distance $= 15$ m.
Determining the Direction
The final position is at (15,0) and the starting position is at (0,0). A point with a positive x-coordinate and a zero y-coordinate, relative to the origin, is directly to the East.
Therefore, X is to the East of the starting position.
Combining the distance and direction, X is 15 m east from the starting position.
Summary of Movements
| Step | Movement / Turn | Direction | Distance (m) | Current Position (assuming start at (0,0)) |
|---|---|---|---|---|
| Start | - | - | 0 | (0,0) |
| 1 | Walk South | South | 15 | (0, -15) |
| 2 | Turn Left, Walk | East | 15 | (15, -15) |
| 3 | Turn Left, Walk | North | 15 | (15, 0) |
The final position is (15,0), which is 15 meters to the East of the starting point (0,0).
Revision Table: Key Concepts
| Concept | Explanation |
|---|---|
| Starting Point | The initial location from where movement begins. Often treated as the origin (0,0) in coordinate geometry. |
| Direction | The path taken (North, South, East, West, or intermediate directions). |
| Distance | The length of the path segments or the straight-line distance between two points. |
| Left/Right Turns | Changing direction by 90 degrees from the current facing direction. From North: Left is West, Right is East. From South: Left is East, Right is West. From East: Left is North, Right is South. From West: Left is South, Right is North. |
| Displacement | The straight-line distance and direction from the starting point to the ending point. This is what the question asks for. |
Additional Information: Visualizing Movement
Imagine a grid. Starting at the center (0,0):
- Moving South 15m takes you straight down to (0, -15).
- From there, turning left means facing East. Moving 15m East takes you 15 units to the right, from (0, -15) to (15, -15).
- From there, turning left means facing North. Moving 15m North takes you 15 units up, from (15, -15) to (15, 0).
The final point is clearly located 15 units to the right (East) of the starting point (0,0).
Important Questions from Direction and Distance Stops
Six houses, A, B, C, D, E and F, are situated in a colony. D is 60 m south of E. F is 40 m south of B. A is 30 m north of E. F is 50 m east of A. C is 50 m west of B. Find the location of C with reference to A.
One morning, Chitrashi and Ayaan sit facing each other. If the shadow of Ayaan falls to the left of Chitrashi, then in which direction is Ayaan facing?
The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square.
What should come in place of the question mark (?) in the given series?
28 39 53 70 90 ?Pranay starts from Point A and drives 8 km towards east. He then takes a right turn, drives 11 km, turns right and drives 12 km. He then takes a right turn and drives 13 km. He takes a final right turn, drives 4 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90° turns only unless specified.)
