Question

6. Find the coordinates of the point which is three-fifths of the way from (3,4,5) to (-2,-1,0).
​

Answer 1

Let the coordinate of the point P which is three fifth of the way from A(2,−5) to the point B(−3,5) is (x,y)

Since,

AB

AP

​  

=  

5

3

​  

 

=>  

AP

AB

​  

=  

3

5

​  

 

=>  

AP

AP+BP

​  

−1=  

3

5

​  

−1

=>  

AP

BP

​  

=  

3

2

​  

 

=>  

BP

AP

​  

=  

2

3

​  

 

As we know that if a point P(x,y) divides the line segment AB joining the points A(x  

1

​  

,y  

1

​  

)&B(x  

2

​  

,y  

2

​  

)  in the ratio m:n then, by the section formula, we have

x=  

m+n

nx  

1

​  

+mx  

2

​  

 

​  

&y=  

m+n

ny  

1

​  

+my  

2

​  

 

​  

.

∴  (x,y)=(  

3+2

3×(−3)+2×2

​  

,  

3+2

3×5+2×(−5)

​  

)

               =(  

5

−9+4

​  

,  

5

15−10

​  

)

               =(  

5

−5

​  

,  

5

5

​  

)

                =(−1,1)