Straight Line and Pair of Straight Lines 3 Question 6
7. Given the four lines with the equations
$x+2 y-3=0,3 x+4 y-7=0$,
$2 x+3 y-4=0,4 x+5 y-6=0$, then
(1980, 1M)
(a) they are all concurrent
(b) they are the sides of a quadrilateral
(c) only three lines are concurrent
(d) None of the above
Objective Question II
(One or more than one correct option)
Show Answer
Answer:
Correct Answer: 7. (c)
Solution:
- Given lines, $x+2 y-3=0$ and $3 x+4 y-7=0$ intersect at $(1,1)$, which does not satisfy $2 x+3 y-4=0$ and $4 x+5 y-6=0$.
Also, $3 x+4 y-7=0$ and $2 x+3 y-4=0$ intersect at $(5,-2)$ which does not satisfy $x+2 y-3=0$ and $4 x+5 y-6=0$.
Lastly, intersection point of $x+2 y-3=0$ and $2 x+3 y-4=0$ is $(-1,2)$ which satisfy $4 x+5 y-6=0$. Hence, only three lines are concurrent.
