Final answer:
The mathematics question involves calculating the midpoint between two points on a coordinate grid, determining the net displacement of a delivery man following a specific set of directions, and finding the total displacement vector after walking in certain compass directions, which is addressed using vector addition principles.
Step-by-step explanation:
The question provided seems to be a part of a mathematics problem related to vectors and their representations on a coordinate system. The scenarios described involve understanding vector addition, displacement, and coordinate geometry, which are key concepts covered in high school physics and mathematics. Let's take three different scenarios described and answer them briefly:
- Midpoint Calculation: To find the location of a rest station which is a midpoint between two cities on a coordinate grid, you calculate the average of the x-coordinates and the y-coordinates of the given city locations separately. The midpoint can be found using the formula: Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2).
- Net Displacement Vector: To determine the delivery man's net displacement, you would add each vector that represents his journey's segments, taking into account their directions. For vectors given in compass directions, you must first break them down into their components and then sum these components.
- Displacement After Walking: When you walk in certain compass directions and want to find your final displacement vector, you represent each segment as a vector, convert the compass directions to angles with respect to the coordinate axes, calculate the components for each vector, then sum these components to find the total displacement vector.
These problems are solved by applying the principles of vector addition and understanding the relationships between different vector components and their resultant vectors.