Question

Any line of slope 2 is intercepted by the lines 4x + y 9 = 0, x - 2y + 3 = 0, 5x y - 6 = 0. Prove that the portions intercepted are equal.

Answer 1

Any lines whose slope is 2 is y = 2x + c. Let it meet the given lines in A, B and C respectively. Solving with given lines, we get
$A(\frac{9-c}{6},\frac{9+2c}{3}),B(\frac{3-2c}{3},\frac{6-c}{3})and(\frac{6+c}{3},\frac{12+5c}{3})$
Clearly A is mid - point of BC so that BA = AC
Hence the portious intercepted are equal .