Section Formula


 
 
Concept Explanation
 

Section Formula

Section formula is used to find the coordinates of a point that divides the line segment joining the points in a given ratio.

Internal Division:

Coordinates of point P(x,y) which divides the line segment joining A(x_{1},y_{1})  and B B(x_{2},y_{2}) internally in the ratio m_{1}:m_{2} (m_{1},m_{2}>0) are given by

            x=frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}}

           y=frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}}

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Sample Questions
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Question : 1

 In what ratio does the point P(2, −5) divide the line segment joining A(−3, 5) and B(4, −9) .

Right Option : B
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Question : 2

The coordinates of two points A and B are (2,2) and (8,6) respectively. P is a point on the line AB such that AP: PB = 1: 1, Find the coordinates of P.

Right Option : A
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Explanation
Question : 3

 Find the ratio in which the point (-3,p) divides the line segment joining the points (-6,-4) and (-4,3). Hence, find the value of p.

Right Option : B
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Explanation
 
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