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?


a) components: LeftAngleBracket 28, 25 RightAngleBracket, actual distance: about 37.54 meters
b) components: LeftAngleBracket 28, 25 RightAngleBracket, actual distance: about 3,754 meters
c) components:LeftAngleBracket negative 28, negative 25 RightAngleBracket, actual distance: about 37.54 meters
d) components:LeftAngleBracket negative 28, negative 25 RightAngleBracket, actual distance: about 3,754 meters

Answer:

C: <-28,-25>, etc.

Step-by-step explanation:

The vector from A to B is (-28, -25) and the distance between A to B is 3754 meters.

One of the most intriguing ideas in mathematics is called coordinate geometry. By using graphs with curves and lines, coordinate geometry (also known as the analytic geometry) explains how geometry and algebra are related. They can answer geometrical problems because it gives them geometrical aspects of algebra. In this area of geometry, a pair of ordered numbers is used to describe the location of points on a plane.

As per the given data:

Coordinates of school A =  (7, 12)

Coordinates of school B = (-21, -13)

Scale of the map is 1 unit = 100 m

For vector representing the path A to B:

Final - Initial coordinates

= (-21 - 7, -13 - 12)

= (-28, -25)

Distance between A and B:

Distance formula = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

= [tex]\sqrt{(-21 - 7)^2 + (-13 - 12)^2}[/tex]

= 37.54 units {1 unit = 100 m}

= 3754 meters

Hence, the vector from A to B is (-28, -25) and the distance between A to B is 3754 meters.

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