Question

Find the co-ordinates of the points of trisection of the line joining the points $(-3,0)$ and $(6,6).$

Answer 1

$A(-3,0)B(6,6)$

Let $A(-3,0)$ be the first point and $B(6,6)$ be the second point and $P$ and $Q$ be the internally trisecting point

Let $AB=PQ=QB=K$

$PB=PQ+OB=2K$

And $AQ=AP+PQ=2K$

$AP=PB=1:2$

And $AQ:QB=2:1$

$P$ divides $a,b$ internally in ratio $1:2$ while $Q$ divides internally in the ratio $2:1$ does coordinates of $p$ and $q$ are

$P(\frac{1\left(6\right)+2\times (-3)}{1+2},\frac{1\left(6\right)+2\left(0\right)}{1+2})=P(0,2)$

$Q(\frac{2\left(6\right)+1\times (-3)}{1+2},\frac{2\left(6\right)+1\left(0\right)}{1+2})=Q(\frac{9}{3},\frac{12}{3})=Q(3,4)$

$P(0,2)$ and $Q(3,4)$ are point of trisection