Q. 1 A4.4( 5 Votes )

Prove that the following sets of three lines are concurrent:

15x – 18y + 1 = 0, 12x + 10y – 3 = 0 and 6x + 66y – 11 = 0

Answer :

Given:


15x – 18y + 1 = 0 …… (i)


12x + 10y – 3 = 0 …… (ii)


6x + 66y – 11 = 0 …… (iii)


To prove:


Sets of given three lines are concurrent.


Explanation:


Now, consider the following determinant:


= 15(- 110 + 198) + 18(-132 + 18) + 1(792 – 60)


1320 – 2052 + 732 = 0


Hence proved, the given lines are concurrent.


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