(A) The equation $|x + y + 1| = 4$ represents two parallel lines:$x + y + 1 = 4 \implies x + y - 3 = 0$$x + y + 1 = -4 \implies x + y + 5 = 0$For the

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(A) The equation $|x + y + 1| = 4$ represents two parallel lines:$x + y + 1 = 4 \implies x + y - 3 = 0$$x + y + 1 = -4 \implies x + y + 5 = 0$For the point $(a, 2a)$ to lie between these two lines,the expressions $(x + y - 3)$ and $(x + y + 5)$ must have opposite signs at the point $(a, 2a)$.Substituting $(a, 2a)$ into the expressions:$(a + 2a - 3)(a + 2a + 5) $(3a - 3)(3a + 5) $9(a - 1)(a + 5/3) $(a - 1)(a + 5/3) This inequality holds when $a$ is between the roots:$a \in (-5/3, 1)$

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

If the point $(a, 2a)$ lies between the lines $|x + y + 1| = 4$,then the complete set of values of $'a'$ is:

A
$(-5/3, 1)$
B
$(1, 5/3)$
C
$(-4/3, 4/3)$
D
$(-\infty, -5/3) \cup (1, \infty)$

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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 point $(a, 2a)$ lies between the lines $|x + y + 1| = 4$,then the complete set of values of $'a'$ is:

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