Answer :

Given:

A = (– 6, 10)


B = (3, –8)


P = (–4, 6)


Let the ratio in which P (–4, 6) divides the line segment joining the points A (– 6, 10) and B (3, –8) be k: 1


We know that by Section formula,




This gives 2 equations,


1.



-4(k + 1) = 3k + (-6)


-4k – 4 = 3k – 6


3k – 6 + 4k + 4 = 0


7k – 2 = 0



2.



6(k + 1) = -8k + 10


6k + 6 = -8k + 10


6k + 6 + 8k – 10= 0


14k – 4 = 0



Hence, Ratio = 2: 7


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