Question

The post office is to the east of the school while my house is to the south of the school. The market is to the north of the post office. If the distance of the market from the post office is equal to the distance of my house from the school, in which direction is the market with respect to my school?

• A. South-west
• B. North-east
• C. North
• D. East

Hint:

Using a simple coordinate plane (\(x, y\)) with the starting point at the origin \( (0,0) \) is the most foolproof way to solve complex direction and distance problems.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This is a direction sense problem involving relative positions and distances. We need to find the final direction of the market relative to the school based on the given geographical placements.


Step 2: Key Formula or Approach:
We can map the locations on a standard Cartesian coordinate system (x, y), where the 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 3: Detailed Explanation:
Let the school be located at the origin \( (0, 0) \).
1. The post office is to the east of the school. Let its coordinates be \( (d, 0) \), where \( d > 0 \).
2. The house is to the south of the school. Let its coordinates be \( (0, -y) \), where \( y > 0 \). The straight-line distance from the house to the school is simply \( y \).
3. The market is to the north of the post office. Since it is directly north of the post office \( (d, 0) \), its x-coordinate remains \( d \). Let its coordinates be \( (d, m) \), where \( m > 0 \). The straight-line distance from the market to the post office is \( m \).
We are explicitly given that the distance of the market from the post office equals the distance of the house from the school. Therefore, \( m = y \).
So, the market is located exactly at the coordinate \( (d, y) \).
Now, we need to find the direction of the market \( (d, y) \) with respect to the school \( (0, 0) \).
Since \( d > 0 \) (indicating East) and \( y > 0 \) (indicating North), the vector pointing from the school to the market lies squarely in the first quadrant.
This combined direction corresponds to North-east.


Step 4: Final Answer:
The market is in the North-east direction with respect to the school.