The line segment AB is divided into five congruent parts at P,Q,R and S such that `A-P-Q-R-S-B`. If point `Q(12,14)` and `S(4,18)` are given find the coordinates of A, P,R,B.

Explanation

`Q(12,14)` and `S(4,18)`
Let `A(x_(1),y_(1)),P(x_(2),y_(2)),R(x_(3),y_(3))` and `B(x_(4),y_(4))`
Q is the midpoint of AS
`:.` by midpoint formula,
`12=(x_(1)+4)/2, 14=(y_(1)+18)/2`
`:.x_(1)+4=12xx2, :.y_(1)+18=14xx2`
`:.x_(1)+4=24, :.y_(1)+18=28`
`:.x_(1)=24-4, :.y_(1)=28-18`
`:.x_(1)=20, :.y_(2)=10`
The coordinates of point A are `(20,10)`.
`P` is the midpoint of seg AQ.
`:.` by midpoint formula,
`x_(2)=(20+12)/2, y_(2)=(10+14)/2`
`:.x_(2)=32/2, :.y_(2)=24/2`
`:.x_(2)=16, :.y_(2)=12`
`:.` the coordinates of point `P` are (16,12)
R is the midpoint of seg QS.
`:.` by midpoint formula, ltbRgt `x_(3)=(12+4)/2, y_(3)=(14+18)/2`
`:.x_(3)=16/2, :.y_(3)=32/2`
`:.x_(3)=8,:.y_(3)=16`
`:.` the coordinates of point R are (8,16).
S is the midpoint of seg RB.
`:.` by midpoint formula,
`4=(8+x_(4))/2, 18=(16+y_(4))/2`
`:.8+x_(4)=4xx2, :.16+y_(4)=18xx2`
`:.8+x_(4)=8, :.16+y_(4)=36`
`:.x_(4)=8-8,:.y_(4)=36-16`
`:.x_(4)=0, :.y_(4)=20`
`:.` the coordinates of point B are (0,20).
The coordinates of point A are (20,10), the coordinates of point P are (16,12), the coordinates of point R are (8,16) and the coordinates of point B are (0,20).