Question

A tourist information center is between a bus station and a train station. When mapped on a grid, the tourist information center is located at (1,4) and the bus is located at (-3,7) The train station is located at point

Answer 1

Answer: The train station is located at point (5,1).

Explanation:

Given: On a grid, information center is located at (1,4) and the bus is located at (-3,7).

A tourist information center is between bus station and train station.

i.e. tourist information center is a mid point of line joining bus station and train station.

Midpoint between (a,b) and (c,d) is given by :-

`(x,y)=((a+c)/(2),(b+d)/(2))`

Let (a,b) be the coordinates of train station , then

`(1,4)=((-3+a)/(2),(7+b)/(2))\\\\\Rightarrow\ 1=(-3+a)/(2)\ \ \ , 4=(7+b)/(2)\\\\\Rightarrow\ 2=-3+a\ \ \ , 8=7+b\\\\\Rightarrow\ 2+3=a\ \ \ , 8-7=b\\\\\Rightarrow a= 5,\ \ b=1`

Hence, the train station is located at point (5,1).