Point C (4,2) divides the line segment joining points A(2, -1) and B (x,y) such that AC:C8 = 3:1. What are the coordinates of point B?
+128475 We can solve this as follows :
Since AC:CB = 3:1......then C is 3/4 the distance from A to B
The x coordinate of B is found as
[ ( + (3/4) (x - 2) ] = 4
2 + (3/4)x - 3/2 = 4
1/2 + (3/4)x = 8/2 subtract 1/2 from both sides
(3/4)x = 7/2 multiply both sides by 4/3
x = 28/6 = 14/3 = x coordinate of B
The y coordinate of B is found as
[ -1 + (3/4) ( y - -1) ] = 2
-1 + (3/4)y + 3/4 = 2
-1/4 + (3/4)y = 2
-1/4 + (3/4)y = 8/4 add 1/4 to both sides
(3/4)y = 9/4
3y = 9
y = 3
So....the coordinates of B are ( 14/3 , 3)
