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# The line segment joining A(-1,5/3) the points B (a, 5) is divided in the ratio 1 : 3 at P, the point where the line segment AB intersects y-axis. Calculate (i) the value of a (ii) the co-ordinates of P.

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An Important Question of class 10 Based on Section Formula Chapter of M.L Aggarwal for ICSE BOARD.
Given that a line segement joining points is divided in a ratio at a pooint. Solve this question
This is the Question Number 14, Exercise 11 of M.L Aggarwal.

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1. (i) Let P(x,y) divides the line segment joining the points A(-1,5/3), B(a,5) in the ratio 1:3,

Here m:n = 1:3

x1 = -1 , y1 = 5/3 , x2 = a, y2 = 5

By Section formula x = (mx2+nx1)/(m+n)

x = (1×a+3×-1)/(1+3)

x = (a-3)/4

x = (a-3)/4 …..(i)

By Section formula y = (my2+ny1)/(m+n)

y = (1×5+3×5/3)/(3+1)

y = (5+5)/4

y = 10/4

y = 5/2 ….(ii)

Given P meets Y axis. So its x co-ordinate will be zero.

i.e, (a-3)/4 = 0

a-3 = 0

a = 3

(ii) x = (a-3)/4 [From (i)]

Substitute a = 3 in above equation.

x = (3-3)/4 = 0

y = 5/2 [From (ii)]

Hence the co-ordinates of P are (0,5/2).

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