(B) Let $f(x, y) = 3x - 5y + a$. For the points $(1, 2)$ and $(3, 4)$ to lie on the same side of the line,$f(1, 2)$ and $f(3, 4)$ must have the same s

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(B) Let $f(x, y) = 3x - 5y + a$. For the points $(1, 2)$ and $(3, 4)$ to lie on the same side of the line,$f(1, 2)$ and $f(3, 4)$ must have the same sign. $f(1, 2) = 3(1) - 5(2) + a = a - 7$ $f(3, 4) = 3(3) - 5(4) + a = a - 11$ Thus,$(a - 7)(a - 11) > 0$. Solving this inequality,we get $a 11$. Therefore,$a \in (-\infty, 7) \cup (11, \infty)$,which is $R - [7, 11]$.

Class 11 Mathematics Straight Line Distance between two lines, Perpendicular distance of the line from a point, Position of point w.r.t. line

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If the points $(1, 2)$ and $(3, 4)$ lie on the same side of the straight line $3x - 5y + a = 0$,then $a$ lies in the set

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A
$[7, 11]$
B
$R - (7, 11)$
C
$[7, \infty)$
D
$(-\infty, 11]$

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Class 11

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Straight Line

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Distance between two lines, Perpendicular distance of the line from a point, Position of point w.r.t. line

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If the points $(1, 2)$ and $(3, 4)$ lie on the same side of the straight line $3x - 5y + a = 0$,then $a$ lies in the set

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