Question

Find the points which divide the line segment joining $A(-11,4)$ and $B(9,8)$ into four equal parts.

Answer 1

Let $P,Q,R$ be the points on the line segment joining $A(-11,4)$ and $B(9,8)$ such that $AP=PQ=QR=RB$

Here $Q$ is the mid-point of $AB,P$ is the mid-point of $AQ$ and $R$ is the mid-point of $QB$.
$Q$ is the mid-point of $AB=(\frac{-11+9}{2},\frac{4+8}{2})=(\frac{-2}{2},\frac{12}{2})=(-1,6)$
$P$ is the mid-point of $AQ=(\frac{-11-1}{2},\frac{4+6}{2})=(\frac{-12}{2},\frac{10}{2})=(-6,5)$ $R$ is the mid-point of $QB=(\frac{-1+9}{2},\frac{6+8}{2})=(\frac{8}{2},\frac{14}{2})=(4,7)$
Hence the points which divides $AB$ into four equal parts are $P(-6,5),Q(-1,6)$ and $R(4,7)$.