Prove that the following sets of three lines are concurrent: 15x – 18y + 1 = 0, 12x + 10y – 3 = 0 and 6x + 66y – 11 = 0

Question

Philoid · Accepted 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.