Question

3. Find the coordinates of the points P,Q and R which divide the line segment joining A(5,4) and B(11,6) into

four equal parts.

​

Answer 1

Answer:

Step-by-step explanation:

Given: Points P, Q and R in order divide a line segment joining the points A(1,6) and B(5,−2) in four equal parts.

Using formula:

x=  

m  

1

​  

+m  

2

​  

 

m  

1

​  

x  

2

​  

+m  

2

​  

x  

1

​  

 

​  

 

y=  

m  

1

​  

+m  

2

​  

 

m  

1

​  

y  

2

​  

+m  

2

​  

y  

1

​  

 

​  

 

Step 1: Find coordinates of P.

P(x,y) divides AB in the ratio of 1:3

x=(5+3)/4=8/4=2

y=(−2+18)=16/4=4

So, P(x,y)=P(2,4)

Step 2: Find coordinates of Q.

Q divides the segment AB in ratio 2:2 or 1:1. So Q is a mid point of AB

So, Q((1+5)/2,(6−2)/2)=(3/2)

So, Q(x,y)=Q(3,2)

Step 3: Find coordinates of R.

R divides the segment AB in ratio 3:1

x=(3×5+1×1)/4

=4

y=(3×(−2)+1×6)/4

=0

So, R(x,y)=R(4,0).