Question

The line AB is trisected by the points (2, 3) and (5, 4). Find the coordinates of the points A and B.
​

Answer 1

Answer:

its the the answer of similar ques

Explanation:

Let A and B be (2,1) and (5,−8) respectiviey

∴  

AB

AP

​  

=  

2

1

​  

 

Section Formula: If point (x,y) divides line joining two points in (x  

1

​  

,y  

1

​  

) and (x  

2

​  

,y  

2

​  

) in ratio m:n internally

⇒ x=  

m+n

mx  

2

​  

+nx  

1

​  

 

​  

y=  

m+n

my  

2

​  

+ny  

1

​  

 

​  

 

Here, x  

1

​  

=2,y  

1

​  

=1, x  

2

​  

=5,y  

2

​  

=−8 and m=1,n=2

⇒ x=  

3

5+4

​  

=3y=  

3

−8+2

​  

=−2

(x,y)=(3,−2)

The point lies on

⇒ 2x−y+k=0

⇒ 6+2+k=0

⇒ k=−8