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.
Deepak BoraNewbie
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.
Share
(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).