Question

The highway map below shows the two exits between Tomstown (2,3) and Mount Lookout (78,71). Exit 1 is halfway between Tomstown and Mount Lookout. Exit 2 is halfway between Exit 1 and Mount Lookout. What are the coordinates of Exit 2?F.(40,37) G.(74,37) H.(59,54) J.(68,54)

Answer 1

First, we compute the coordinates of Exit 1. According to the problem, Exit 1 is halfway between Tomstown and Mount Lookout, using the formula to compute the coordinates of the midpoint of a segment we get:

`\begin{gathered} x_1=(2+78)/(2)=(80)/(2)=40, \\ y_1=(3+71)/(2)=(74)/(2)=37. \end{gathered}`

Now, since Exit 2 is halfway between Exit 1 and Mount Lookout, we use the same formula as above and get:

`\begin{gathered} x_2=(40+78)/(2)=(118)/(2)=59, \\ y_2=(37+71)/(2)=(108)/(2)=54. \end{gathered}`

Answer: (59,54).