Given the points A(-8,-7) and B(8,5) find the coordinates of point P on directed line segment AB that partitions AB into the ratio 3:1
step 1
Find the distance in the x-coordinate between A and B
dABx=(8-(-8)=8+8=16 units
Find the distance in the y-coordinate between A and B
dABy=5-(-7)=5+7=12 units
step 2
we know that
point P on directed line segment AB that partitions AB into the ratio 3:1
so
AP/AB=3/(3+1)
AP/AB=3/4
Find the x coordinate of point P
APx/ABx=3/4
substitute
APx/16=3/4
APx=16*(3/4)
APx=12 units
The x-coordinate of P is
Px=Ax+APx
where
Ax is the x-coordinate of P
Px=-8+12=4
step 3
Find the y-coordinate of P
we have that
APy/ABy=3/4
substitute
APy/12=3/4
APy=12*(3/4)
APy=9
The y coordinate of P is
Py=APy+Ay
where
Ay is the y-coordinate of P
Py=9+(-7)=2
therefore
the answer is
The coordinate of P are (4,2)