What are the coordinates of the point on the directed line segment from (−7,2) to (4,−9) that partitions the segment into a ratio of 6 to 5?
+129630 The coordinates of the point are given by :
[ − 7 + ( 4 − −7)(6/11) , 2 + ( −9 − 2 ) (6/11) ] =
[ −7 + (11)(6/11) , 2 + (−11) (6/11) ] = ( −7 + 6 , 2 − 6 ) =
( −1 , − 4 )
Proof.....distance from (−7,2) to ( −1,− 4 ) = √ [ ( − 1 − −7)^2 + ( −4 − 2)^2] =
√ [ ( 6)^2 + ( −6)^2] = √72 = 6√2 (1)
And....distance from ( −1,− 4 ) to ( 4,− 9 ) = √ [ ( 4 − −1)^2 + ( −9 − − 4)^2] =
√ [(5)^2 + ( −5)^2 ] = √ [ 25 + 25] = √50 = 5√2 (2)
And the ratio of (1) to (2) = 6√2 : 5√2 = 6 : 5
