An 80-mile trip is represented on a gridded map by a directed line segment from point M(3,2) to point N(9,13). What point represents 60 miles into the trip?
The desired point is ( 60/80) = 6/8 = 3/4 the distance between M and N
To find this point, we have
[ 3 + (3/4)(9 - 3) , 2 + (3/4) ( 13 - 2) ] =
[ 3 + (3/4)(6) , 2 + (3/4)(11) ] =
[ 3 + 18/4 , 2 + 33/4 ] =
[ 12/4 + 18/4 , 8/4 + 33/4 ] =
[30/4 , 41/4 ] =
( 15/2, 41/4)
