Class 10

Math

All topics

Coordinate Geometry

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

Given: Points P, Q, R and S divides a line segment joining the points $A(1,2)$ and $B(6,7)$ in $5$ equal parts. We know that:

$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} $

Now,

Step $1$: Find coordinates of P.

$P(x,y)$ divides AB in the ratio $1:4$

$x=(1×6+4×1)/1+4$

$=(6+4)/5$

$=10/5$

$=2$

$y(1×7+4×2)/5$

$=(7+8)/5$

$=15/5$

$=3$

So, $P(x,y)=P(2,3)$

Step $2$: Find coordinates of Q.

Q divides the segment AB in ratio $2:3$

$x=(2×6+3×1)/5$

$=(12+3)/5$

$=15/5=3$

$y=(2×7+3×2)/5$

$=(14+6)/5$

$=20/5=4$

So, $Q(x,y)=Q(3,4)$

Step $3$: Find coordinates of R.

R divides the segment AB in ratio $3:2$

$x=(3×6+2×1)/5$

$=(18+2)/5$

$=20/5$

$=4$

$y=(3×7+2×2)/5$

$=(21+4)/5$

$=25/5$

$=5$

So, $R(x,y)=R(4,5)$.