Question

if a line segment AB is trisectat then the respective rations will be ______and_____​

Answer 1

Answer

Let the coordinate of point B is (x,y)

Let the point P(3,5) divides the line segment which joins A(-2,3) and B (x,y) in the ration 4:7 internally

so, x  

1

​  

=−2, y  

1

​  

=3, m  

1

​  

=4

x  

2

​  

=−x, y  

2

​  

=y, m  

2

​  

=7

By section formula,

x=  

m  

1

​  

+m  

2

​  

 

m  

1

​  

x  

2

​  

+m  

2

​  

x  

1

​  

 

​  

 

3=  

4+7

(4)(x)+(7)(−2)

​  

 

3=  

11

4x−14

​  

 

4x−14=33

4x=33+14

x=  

4

47

​  

 

And

y=  

m  

1

​  

+m  

2

​  

 

m  

1

​  

y  

2

​  

+m  

2

​  

y  

1

​  

 

​  

 

y=  

4+7

(4)(y)+(7)(3)

​  

 

5=  

11

4y+21

​  

 

4y=55−21

y=  

4

34

​  

=  

2

17

​  

 

Hence the co-ordinate of point B = (  

4

47

​  

,  

2

17

​  

)