Point A is 30 m to the east of Point B. Point C is 43 m to the south of Point A. Point C is 45 m to the east of Point D. Point E is 14 m to the south of Point D. Point F is 35 m to the east of Point E. In which direction is Point B with respect to Point F?
North-west
Understanding the Directional Puzzle
This question asks us to determine the direction of one point (Point B) relative to another point (Point F) based on a series of positional statements. This type of problem requires visualizing or mapping out the locations of the points based on the given directions and distances.
Mapping the Points Step-by-Step
Let's break down the given information and trace the path from one point to the next. We can imagine a coordinate system to help us, although a simple sketch or relative positioning is often sufficient. Let's assume positive x is East and positive y is North.
- Point A is 30 m to the east of Point B.
This means if we start at B and move 30m East, we reach A.
- Point C is 43 m to the south of Point A.
From A, move 43m South to reach C.
- Point C is 45 m to the east of Point D.
This means D is 45m to the west of C.
- Point E is 14 m to the south of Point D.
From D, move 14m South to reach E.
- Point F is 35 m to the east of Point E.
From E, move 35m East to reach F.
Calculating Relative Positions (Using a Coordinate System)
Let's assign coordinates to the points, assuming Point B is at the origin (0, 0). East is the positive x-direction, and North is the positive y-direction.
| Point | Relative to | Direction | Distance (m) | Coordinate (x, y) |
|---|---|---|---|---|
| B | - | - | - | \((0, 0)\) |
| A | B | East | 30 | \((0+30, 0) = (30, 0)\) |
| C | A | South | 43 | \((30, 0-43) = (30, -43)\) |
| D | C | West (since C is East of D) | 45 | \((30-45, -43) = (-15, -43)\) |
| E | D | South | 14 | \((-15, -43-14) = (-15, -57)\) |
| F | E | East | 35 | \((-15+35, -57) = (20, -57)\) |
Now we have the coordinates for Point B \((0, 0)\) and Point F \((20, -57)\).
Determining the Direction of Point B with respect to Point F
We want to find the direction from F to B. This is the direction one would travel starting from F to reach B.
The relative position of B from F is given by the vector \(\vec{FB} = B - F\).
\(\vec{FB} = (0 - 20, 0 - (-57))\)
\(\vec{FB} = (-20, 57)\)
The resulting vector \((-20, 57)\) has:
- A negative x-component (-20): This indicates movement towards the West.
- A positive y-component (57): This indicates movement towards the North.
Combining these, the direction of Point B with respect to Point F is North-west.
Conclusion on Directional Reasoning
By carefully following the steps and either sketching the relative positions or using coordinates, we can accurately determine the final direction. Point B is located North-west of Point F.
Revision Table: Key Directional Terms
| Direction | Description | Coordinate Change (relative) |
|---|---|---|
| North | Towards the top of a map | Positive y |
| South | Towards the bottom of a map | Negative y |
| East | Towards the right of a map | Positive x |
| West | Towards the left of a map | Negative x |
| North-east | Between North and East | Positive x, Positive y |
| North-west | Between North and West | Negative x, Positive y |
| South-east | Between South and East | Positive x, Negative y |
| South-west | Between South and West | Negative x, Negative y |
Additional Information: Tips for Directional Problems
Direction and distance problems are common in reasoning sections. Here are some tips:
- Draw a Diagram: A simple sketch is often the easiest way to visualize the relationships between points. Use arrows to show the direction of movement.
- Use a Reference Point: Start from a known point and plot others relative to it.
- Consider Relative vs. Absolute Direction: Pay close attention to phrases like "X is to the direction of Y" (relative direction from Y to X) versus stating an absolute direction.
- Break Down Complex Paths: Follow the path step-by-step, updating the position after each instruction.
- Practice: The more you practice, the better you become at visualizing these spatial relationships.
Similar Questions
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Important Questions from Direction and Distance Stops
Radha walks 14 km towards north. She turns right and walks 22 km. She turns right and walks 24 km. She turns left and walks 26 km. She finally rotates by an angle of 90 degrees in anti-clockwise direction and walks 24 km. How far and in which direction is her starting point from the finishing point.
Harish wants to meet his friend Farhan. He travels 10 km north and then turns right and travels 2 km. He then goes east for 5 km before reaching Farhan's home. How many km does he travel?
The distance between Nalini and Pramod is 50 m and that between Sarayu and Ravali is 40 m. Sarayu is to the west of Ravali, who is to the east of Nalini at a distance of 70 m. Pramod is to the west or northwest or north of Sarayu.
If Sarayu is to the south of Pramod, what is the distance between Pramod and Sarayu?
Kiran was standing on the way after sunrise. Narmada who was coming from the opposite direction, saw that the shadow of Kiran was falling on his left. So to which direction was Kiran's face?
(Kiran was looking)
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.
