Find the point R that breaks the directed segmentre in a ratio of 1:3. given point P(-4,5) and point Q(4,1).
we have that
PR/RQ=1/3
or
PR/PQ=1/(1+3) ------> PR/PQ=1/4
step 1
Find the horizontal distance between P and Q (PQx)
PQx=4-(-4)=8 units
we hve
PRx/PQx=1/4
solve for PRx (horizontal distance between P and R)
PRx=PQx/4 -------> PRx=8/4=2
Find the x-coordinate of point R (Rx)
Rx=Px+PRx -----> Rx=-4+2=-2
the horizontal coordinate of R is -2
step 2
Find the vertical distance between P and Q (PQy)
PQy=5-1=4 units
we have
PRy/PQy=1/4
solve for PRy (vertical distance between P and R)
PRy=PQy/4 -----> PRy=4/4=1
Find the y-coordinate of point R (Ry)
Ry=Py-PRy ------> Ry=5-1=4
the y-coordinate of R is 4
therefore
the coordinates of point R are (-2,4)