If the point - falls between the lines -x-y-4- then

The correct option is B |α|Given |x+y|=4 The equations of the lines are x+y=4 and x+y= 4 . nbsp;Since, (α,α) lies between these lines ⇒( ...

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Standard XII

Mathematics

Trigonometric Ratios of Common Angles

If the point ...

Question

If the point $(α, α)$ falls between the lines $| x + y | = 4,$ then

| α | = 4

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| α | = 2

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| α | < 2

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| α | < 4

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Solution

The correct option is B $| α | < 2$
Given $| x + y | = 4$
The equations of the lines are $x + y = 4$ and $x + y = - 4$ .
Since, $(α, α)$ lies between these lines
$\Rightarrow (α + α - 4) (α + α + 4) < 0$
$\Rightarrow (2 α - 4) (2 α + 4) < 0$
$\Rightarrow (α - 2) (α + 2) < 0$
$\Rightarrow - 2 < α < 2$
$\Rightarrow | α | < 2$

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If the point (α,α) falls between the lines |x+y|=4, then

The correct option is B |α|<2Given |x+y|=4The equations of the lines are x+y=4 and x+y=−4. Since,(α,α) lies between these lines⇒(α+α−4)(α+α+4)<0⇒(2α−4)(2α+4)<0⇒(α−2)(α+2)<0⇒−2<α<2⇒|α|<2

If the point $(α, α)$ falls between the lines $| x + y | = 4,$ then