If A(-14,-10) , B (6,-2) is given . Find the coordinates of points
which divide segment AB into four equal points .

Explanation

`A(-14,-10)` and `B(6,-2)`
Let P,Q and R be the points that divide segment AB into four equal parts.
Let `P(x_(1)y_(1)),Q(x_(2),y_(2))` and `R(x_(3),y_(3))`.
Q is the midpoint of seg AB.
`:.` by midpoint formula,
`x_(2)=(-14+6)/2,y_(2)=(-10+(-2))/2`
`:.x_(2)=(-8)/2, :.y_(2)=(-12)/2`
`:.x_(2)=-4, :.y_(2)=-6`
The coordinates of point Q are `(-4,-6)`.
P is the midpoint of seg AQ.
`:.` by midpoint formula,
`x_(1)=(-14+(-4))/2, y_(1)=(-10+(-6))/2`
`:.x_(1)=(-18)/2, :.y_(1)=(-16)/2`
`:.x_(1)=-9,:.y_(1)=-8`
`:.` the coordinates of point P are `(-9,-8)`.
R is the midpoint of set QB.
`:.` by midpoijnt formula
`x_(3)=(-4+6)/2, y_(3)=(-6+(-2))/2`
`:.x_(3)=2/2, :.y_(3)=(-8)/2`
`:.x_(3)=1, :.y_(3)=-4`
`:.` the coordinates of point R are (1,-4).
The coordinates of the points which divide segment AB into four equal parts are `(-9,-8),(-4,-6)` and `(1,-4)`.