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Maths-

General

Easy

Question

Lines q and r in the xy-plane are perpendicular and intersect at the origin. If line r passes through (1, k), what is the equation of line q ?

$y = - k x$
$y = \frac{- x}{k}$
$y = \frac{1 - x}{k}$
$y = x - \frac{1}{k}$

The correct answer is: $y equals fraction numerator negative x over denominator k end fraction$

let the equations of lines passing through origin will be y = M₁ x and y = M₂ x
be the lies q and r respectively.
Step 1 :- Find M₂ in terms of k using (1, k)
y = M₂ x ⇒ k = M₂ (1) ⇒ M₂ = k
Step 2 :- find the slope M1 in terms of k using perpendicular condition
Then M₁ × M₂ = - 1 ⇒ k × M₂ = - 1M₂ = - $1 over k$
Step 3 :- find the equation of line q.
y = M₂ x and substitute M₂ = - $fraction numerator 1 space over denominator k end fraction$
∴ y = - $x over k$

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