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Collinearity Condition

If the point ...

Question

If the point P (m , 3) lies on the line segment joining the points $A (- \frac{2}{5}, 6)$ and B (2, 8), find the value of m.

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Solution

equation of line joining AB is
$y minus y subscript 1 equals open square brackets fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction close square brackets open parentheses x minus x subscript 1 close parentheses y minus 6 equals open square brackets fraction numerator 8 minus 6 over denominator 2 minus open parentheses negative begin display style 2 over 5 end style close parentheses end fraction close square brackets open parentheses x plus 2 over 5 close parentheses y minus 6 equals 5 over 6 open parentheses x plus 2 over 5 close parentheses 6 y minus 36 equals 5 x plus 2 6 y minus 5 x minus 38 equals 0 sin c e space p left parenthesis m comma 3 right parenthesis space l i e s space o n space t h e space l i n e space comma s o space i t space m u s t space s a t i s f y space t h e space e q u a t i o n space o f space l i n e space A B 6 left parenthesis 3 right parenthesis minus 5 left parenthesis m right parenthesis minus 38 equals 0 18 minus 38 minus 5 m equals 0 minus 5 m equals 20 m equals negative 4$

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p

divides the line segment joining the points

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B (9, 8)

\frac{A P}{B P} = \frac{K}{1} .

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Q. Point P divides the line segment joining the points A(-1,3) and B(9,8) such that AP/PB=k/1. If P lies on line x-y+2=0 , find the value of k.

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Collinearity Condition

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