An Important Question of class 10 Based on Section Formula Chapter of M.L Aggarwal for ICSE BOARD.

Here two co-ordinates points are given and ration of sides are given .

Solve this question.

This is the Question Number 02, Exercise 11 of M.L Aggarwal.

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# The co-ordinates of two points A and B are ( – 3, 3) and (12, – 7) respectively. P is a point on the line segment AB such that AP : PB = 2 : 3. Find the co-ordinates of P.

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Let the co-ordinates of P(x, y) divides AB in the ratio m:n.

A

(-3,3)and B(12,-7)are the given points.Given m:n = 2:3

x

_{1}= -3 , y_{1}= 3 , x_{2}= 12 , y_{2}= -7 , m = 2 and n = 3By Section formula x = (mx

_{2}+nx_{1})/(m+n)x = (2×12+3×-3)/(2+3)

x = (24-9)/5

x = 15/5

x = 3

By Section formula y = (my

_{2}+ny_{1})/(m+n)y = (2×-7+3×3)/5

y = (-14+9)/5

y = -5/5

y = -1

Hence the co-ordinate of point P are (3,-1).