+0  
 
0
38
1
avatar

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?

 Feb 20, 2020
 #1
avatar+109450 
+1

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)

 

 

cool cool cool

 Feb 20, 2020

18 Online Users

avatar