Question

Points P, Q, R and S divide the line segment joining the points A(1,2) and B(6,7) in 5 equal parts.Find the coordinates of the points P, Q and R.​

Answer 1

Answer:

P, Q, R, S divide the line segment AB on the ratio 1:4,2:3,3:2,4:1 respectively.

From above P divides AB in 1:4 ratio  

coordinates of P using section formula,

m+n

mx  

2

​

+nx  

1

​

 

​

,  

m+n

my  

2

​

+ny  

1

​

 

​

 

here m=1 and n=4,x  

1

​

=1,x  

2

​

=6,y  

1

​

=2,y  

2

​

=7  

⇒  

5

6+4

​

,  

5

7+8

​

 

⇒(2,3)= coordinates of P

Similarly,  

Coordinates of Q,

Q divide AB in 2:3 ratio,

⇒  

5

12+3

​

,  

5

14+6

​

 

⇒ (3,4)= coordinates of Q

Similarly,

R divide AB in 3:2 ratio,

Coordinates of R,

⇒  

5

18+2

​

,  

5

21+4

​

 

⇒ (4,5)= coordinates of R

Step-by-step explanation: