A high school soccer team is going to Columbus to see a professional soccer game. A coordinate grid is superimposed on a highway map of Ohio. The high school is at point (3, 4) and the stadium in Columbus is at point (7, 1). The map shows a highway rest stop halfway between the cities. What are the coordinates of the rest stop? What is the approximate distance between the high school and the stadium? (One unit = 6.4 miles.)

a) The coordinates of the rest stop is .

b) The approximate distance between the high school and the stadium is 32 miles.

Step-by-step explanation:

a) The rest stop is located in the midpoint of the line segment between the high school and the stadium. Vectorially speaking, we use the following formula:

(1)

Where:

- Coordinates of the high school.

- Coordinates of the stadium.

- Coordinates of the rest stop.

If we know that and , then the coordinates of the rest stop are, respectively:

The coordinates of the rest stop is .

b) The approximate distance between the high school and the stadium (), in miles, is the product of the Length Equation of the Line Segment and the scale factor:

(2)

Where:

- Scale factor, in miles.

, - Horizontal and vertical distances between the high school and the stadium, no unit.

If we know that , and , then the distance between the high school and the stadium is:

The approximate distance between the high school and the stadium is 32 miles.

tangent

step-by-step explanation: