A surveyor is studying a map of the community and is using vectors to determine the distance between two schools. on the map, the surveyor determined that school a is at (7, 12), and school b is at (–21, –13). the scale of the map is 1 unit = 100 meters. which vector represents the path from school a to school b, and what is the actual distance between them?

According to the description of the map and the location of the coordinates, it can be established that the vector that represents the path from school a to school b is (-28, -25) and the real distance between them is 3,754 meters (option D)

How to calculate the distance and the vector that separates both schools?

To know the vector that separates both schools, it is necessary to take into account where the starting point is and where the end point is. We must also take into account the displacement in the y-axis and the x-axis.

So, on the y-axis, we need to move from position 7 to position -21, so there is a separation of -28 units.

On the other hand, on the x axis we must move from position 12 to -13, that is, there is a separation of -25 units.

According to the above, the vector that separates both schools is (-28, -25). On the other hand, to calculate the distance, keep in mind that each unit is equal to 100 meters.

So we draw a straight line from point a to point b and multiply by 100 to find the actual distance between the two schools.

Note: This question is incomplete because the options are missing. Here are the options:

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