(C) The equation $|x+y|=4$ represents two parallel lines: $x+y=4$ and $x+y=-4$. For a point $(a, a)$ to lie between these two lines,the expression $(x

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(C) The equation $|x+y|=4$ represents two parallel lines: $x+y=4$ and $x+y=-4$. For a point $(a, a)$ to lie between these two lines,the expression $(x+y)$ evaluated at $(a, a)$ must lie between the values $-4$ and $4$. Substituting $(a, a)$ into the expression $x+y$,we get $a+a = 2a$. Thus,the condition is $-4 Dividing the inequality by $2$,we get $-2 This is equivalent to $|a| < 2$.

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 a point $(a, a)$ lies between the lines $|x+y|=4$,then

AP EAMCET 2021 All AP EAMCET

A
$|a|=2$
B
$|a|=3$
C
$|a| < 2$
D
$|a| < 3$

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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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