Class 10

Math

All topics

Coordinate Geometry

Points P, Q and R in that order are dividing a line segment joining $A(1,6)$ and $B(5,−2)$ in four equal parts. Find the coordinates of P, Q and R.

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