Q) The line segment joining the points A(4,-5) and B(4,5) is divided by the point P such that AP : AB = 2 : 5. Find the coordinates of P.
Ans: Let’s draw the diagram to solve:
Given that 
(AB = AP + PB)
by cross multiplication, we get: 5 AP = 2 (AP + PB)
or
By section formula, if a point (x, y) divides the line joining the points (x1, y1) and (x2, y2) in the ratio m : n, then coordinates of point (x, y) =
(
, 
)
Here, it is given that A(4, -5) = (x1, y1) and B(4, 5) = (x2, y2), m : n = 2 : 3
Hence the co-ordinates of point P:
x = 
= 4Similarly, y = 
= -1 Therefore, the coordinates of P are (4, -1)
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(AB = AP + PB)
, 
)
x = 
= 4
= -1