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.
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Important Questions from Direction and Distance Stops
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.)
A child went 90 feet in the west to look for his father, then he turned right and went 20 feet. After this, he turned right and walked 30 feet to reach his uncle's house. His father was NOT there. From there he went 100 feet to his south and met his father. How far did he meet his father from the starting point?
Four friends live in a locality. A's house is to the west of B. B 's house is to the south of C and C's house is to the east of D. In which direction is B's house as to D?
