Point P is located at (2, 2) and point T is located at (7, 17). What are the coordinates of the point that partitions the directed line segment PT in a 3:2 ratio?
+128407 If we have a 3:2 ratio....then PT can be divided into 5 equal parts.....
And the distance from P to the partition point must be 3/5 of the distance from P to T
So....we can find the partition point thusly :
[ x coordinate of P + (3/5) (x coordinate of T - x coordinate of P) , y coordinate of P + (3/5) (y coordinate of T - y coordinate of T ) ] =
[ ( 2 + (3/5)(7 - 2) , 2 + (3/5)(17 - 2)) ] =
[ 2 + (3/5)(5) , 2 + (3/5) (15) ] =
[ 2 + 3 , 2 + 9 ] =
( 5, 11)
