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?
Show 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.
Step 1: Understanding the Question:
This problem is categorized under Direction and Distance Sense. It requires the solver to visualize the relative positions of four different landmarks: a school, a post office, a house, and a market. The key challenge is to place these points correctly on a two-dimensional plane using cardinal directions and then identify the vector (direction) from one specific point to another. It also introduces a condition about equal distances that helps fix the exact coordinates of the points. Step 2: Key Formulas and approach:
The most accurate approach is to use the "Coordinate Geometry" method or a "Standard Direction Compass."
1. Set the primary reference point (the school) at the center or origin $(0, 0)$.
2. Treat North as positive y, South as negative y, East as positive x, and West as negative x.
3. Plot the other points relative to the origin.
4. Once all points are plotted, identify the quadrant where the target point lies to determine its direction relative to the origin. Step 3: Detailed Explanation:
Let's place the School at point $(0, 0)$.
The Post Office is East of the school. Let's assign it coordinates $(D1, 0)$, where $D1$ is any positive horizontal distance.
The House is South of the school. Let's assign it coordinates $(0, -D2)$, where $D2$ is the vertical distance from the school to the house.
The Market is North of the Post Office. Since the Post Office is at $(D1, 0)$, moving North from there changes the y-coordinate. The Market is at $(D1, D3)$, where $D3$ is the distance from the Post Office to the Market.
The problem states that the distance from the Market to the Post Office ($D3$) is equal to the distance from the House to the School ($D2$). So, $D3 = D2$.
The Market's final coordinates are $(D1, D2)$.
Now, we find the direction of the Market $(D1, D2)$ with respect to the School $(0, 0)$.
Since $D1$ is positive (East) and $D2$ is positive (North), the Market is in the upper-right area relative to the school. This specific area between North and East is known as North-east.
Step 4: Final Answer:
The market is in the North-east direction with respect to the school.
