Straight LineMedium
Question
Given the four lines with the equations x + 2 y - 3 = 0, 3x + 4 y - 7 = 0 2x + 3y - 4 = 0, 4x + 5y -6 = 0 then
Options
A.they are all concurrent
B.they are the sides of a quadrilateral
C.only three lines are concurrent
D.None of the above
Solution
Given lines, x + 2y - 3 = 0 and 3x + 4y - 7 = 0 intersect at 91, 10 which does not satisfy 2x + 3y - 4 = 0 and 4x + 5y - 6 = 0 Also, 3x + 4 y - 7 = 0 and 2x + 3y - 4 = 0 intersect at (5,-2) which does not satisfy x + 2 y - 3 = 0 and 4x + 5y - 6 = 0.
Lastly, intersection point of x + 2 y - 3 = 0 and 2x + 3y - 4 = 0 is (-1, 2) which satisfy 4x + 5y - 6 = 0
Hence, only three lines are concurrent.
Lastly, intersection point of x + 2 y - 3 = 0 and 2x + 3y - 4 = 0 is (-1, 2) which satisfy 4x + 5y - 6 = 0
Hence, only three lines are concurrent.
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