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)

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Answer:

Correct Answer: 7. (c)

Solution:

  1. 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.



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