Question

A bus travels through the city and stops every mile. The first stop on the route is the 8th Avenue Coffee Shop, which is located 15 blocks east and 22 blocks north of the central station. The last stop on the route is the airport, which is located 25 blocks west and 36 blocks south of the central station. A student calculated the middle stop along the bus route to be located 20 blocks east and 29 blocks north of the central station. Evaluate the student’s answer.

Answer 1

Answer:Student calculation is incorrect

Step-by-step explanation :

Given the First stop is the 8th Avenue Coffee Shop, which is located 15 Blocks east and 22 blocks north of the central station

and the last stop on the route is 25 blocks west and 36 blocks south of the central station .

Lets take the First stop co-ordinates be (15,22)

and last stop co-ordinates (-25,-30)

So there mid-point is $x=\frac{x_1+x_2}{2}$

$y=\frac{y_1+y_2}{2}$

$x=\frac{15-25}{2}=-5$

$y=\frac{22-30}{2}=-4$

Therefore middle stop is 5 blocks west and 4 blocks South

Thus calculated the middle stop incorrectly.

Answer 2

The student apparently added numbers without taking into account direction. They seem to have added 15 and 25 and divided by 2 to get the horizontal component of the middle stop when they should have added 15 and -25 and divided by 2. A similar mistake was made on determining the vertical component. The middle stop should have been calculated as 5 blocks west and 7 blocks south of the central station. So your answer is C.