(Q29)Find the coordinates of the points which divide the line segment joining A(-4,0) and B(0,6) into four equal parts.

Answer

Given A(-4,0) and B(0,6)

Let P,Q and R be the points which divide AB into four equal parts.

ABPQR(-4,0)(-2,3)(0,6)

P divides AB in the ratio 1:3, Q=1:1 and R=3:1 use section formula to find P,Q and R.

Then, Q is the midpoint of AB.

P is the midpoint of AQ.

R is the midpoint of QB.

Midpoint= (
x1+x2
2
 ,
y1+y2
2
)
Q(x,y)= (
-+
2
 ,
+
2
)
= (
-
2
 ,
2
) =(-,)
P(x,y) = (
-+(-)
2
 ,
+
2
)
= (
-
2
 ,
2
)
= (-,
2
)
R(x,y)=
-+
2
 ,
+
2
= (
-
2
 ,
2
)
= (-,
2
)