Q. Given four lines with equations $x + 2y - 3 = 0,\ 2x + 3y - 4 = 0,\ 3x + 4y - 5 = 0,\$ $4x + 5y - 6 = 0$ These lines are

A) Concurrent
B) The sides of a quadrilateral
C) The sides of a parallelogram
D) The sides of a square
Explanation

(a)
Given equation of line are
$x + 2y - 3 = 0$ …(i)
$2x + 3y - 4 = 0$ …(ii)
$3x + 4y - 5 = 0$ …(iii)
$and\ 4x + 5y - 6 = 0$ …(iv)
On solving Eqs. (i) and (ii), we get
$x = - 1,\ y = 2$
From, Eq. (iii),
$3( - 1) + 4(2) - 5 = 0\ \Rightarrow \ 0 = 0$
From Eq. (iv),
$4( - 1) + 5(2) - 6 = 0\ \Rightarrow \ 0 = 0$
Hence, given lines are concurrent.

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.