The front door of Mr X's house faces East. Mr X leaves the house, walking 50 m straight from the back door that is situated directly opposite to the front door. He then turns to his right, walks for another 50 m and stops. The direction of the point Mr X is now located at with respect to the starting point is ______.
North-West
Let us solve this directional reasoning problem step-by-step to accurately determine Mr X's final position relative to his starting point.
Mr X's Directional Journey Explained
The problem describes Mr X's movement starting from his house and asks for his final direction from the initial point. We need to carefully trace his path, considering the directions and turns.
House Orientation and Starting Direction
- The front door of Mr X's house faces East.
- The back door is situated directly opposite to the front door. This means if the front door faces East, the back door must face West.
- Mr X leaves the house, walking 50 m straight from the back door. Since the back door faces West, Mr X's initial movement is 50 m towards the West.
Tracing Mr X's Path Traversal
Let's represent the starting point of Mr X as the origin (0,0) on a coordinate plane, where East is the positive x-axis, West is the negative x-axis, North is the positive y-axis, and South is the negative y-axis.
Step 1: First Movement
- Mr X walks 50 m straight from the back door.
- Since the back door faces West, this movement is 50 m towards the West.
- After this movement, Mr X's position relative to the starting point is 50 m West.
- In coordinates, if he starts at \((0,0)\), he moves to \((-50, 0)\).
Step 2: Second Movement
- From his current position (50 m West), he then turns to his right.
- When a person is facing West, a right turn means turning towards the North.
- He then walks for another 50 m in this new direction. So, this movement is 50 m towards the North.
- After this movement, Mr X's position is 50 m West and 50 m North from the starting point.
- In coordinates, from \((-50, 0)\), he moves 50 m North to \((-50, 50)\).
Determining Mr X's Final Location Direction
Mr X's final position is \((-50, 50)\) with respect to his starting point \((0,0)\). This means he is:
- 50 m towards the West (negative x-axis direction) from the starting point.
- 50 m towards the North (positive y-axis direction) from the starting point.
When an object is located both West and North of a reference point, its direction from that reference point is North-West.
Relative Direction Outcome
The direction of the point Mr X is now located at with respect to the starting point is North-West. This corresponds to the option provided as the correct answer.
Important Questions from Direction and Distance
- Vijendra walks a certain distance, say X metres, from his home towards the west. Then he turns left and walks 23 metres. After that, he turns left and walks 36 metres. Then he turns left again to walk 23 metres. He finally turns left and walks 18 metres to reach his home. Find the value of X.
Gaurav exits from the backdoor of his north-facing house and walks 25 m straight, then he takes a left turn and walks 36 m, then he turns left and walks 47 m. He turns left again and walks 36 m. How far and in which direction is he from his house now?
Reeta is standing facing south-east. First, she turns 135° clockwise. After that, she turns 90 ° anticlockwise. Then she turns 45 ° clockwise, followed by a 135 ° anticlockwise turn. In which direction is she facing now?
Sahasra started running from her house towards the north. After 40 meters she turned left and ran for 75 meters. She then turned right and ran for 30 meters, and again turned right to run 75 meters. In which direction was she running finally?
At the time of sunset, Lopa and Kritika are sitting facing each other. If the shadow of Lopa falls to the right of Kritika, in which direction is Kritika facing?
