Given the points A(3, 4) and B (6, 10), find the pordinates of the point P on directed line segment AB that partitions AB in the ratio 2:1.
we have that
AP/AB=2/(2+1)
AP/AB=2/3
step 1
Find the distance AB in the x-coordinate (ABx)
ABx=6-3=3 units -----> subtract the x-coordinates
we have that
AP/AB=2/3
so
APx/ABx=2/3
APx is the distance AP in the x-coordinate
substitute the given value in the expression above
APx/3=2/3
APx=2 units
Find the x coordinate of point P
Px=AX+APx
Px=3+2=5
step 2
Find the distance AB in the y-coordinate (ABy)
ABy=10-4=6 units (subtract the y-coordinates)
we have that
AP/AB=2/3
so
APy/ABy=2/3
substitute the given value
APy/6=2/3
APy=4 units
Find the y-coordinate of point P
Py=Ay+APy
Py=4+4=8
therefore
the coordinates of point P are (5,8)