A line AB makes zero intercepts on x-axis and y-axis and it is pe… - Vidyadip

MCQ

A line $AB$ makes zero intercepts on $x$-axis and $y$-axis and it is perpendicular to another line $CD$, $3x + 4y + 6 = 0.$ The equation of line $ AB$ is

A
$y = 4$
B
$4x - 3y + 8 = 0$
✓
$4x - 3y = 0$
D
$4x - 3y + 6 = 0$

✓

Answer

Correct option: C.

$4x - 3y = 0$

c
(c) Given, line $AB$ making $0$ intercepts on x-axis and $y$-axis or $({x_1},\,{y_1}) \equiv (0,\,0)$ and the line is perpendicular to line $CD,\,3x + 4y + 6 = 0$. We know that standard equation of a line is $y = ax + b.$ Comparing given equation of line $CD$ with the standard equation, we get $a = 3$ and $b = 4$.

We also know that slope of the given line $CD = - \frac{a}{b} = \frac{{ - 3}}{4}.$ Since the line $AB$ is perpendicular to the line $CD$, therefore slope of the line $AB(m) = \frac{4}{3}$. Thus relation for the equation of the line $AB$ will be $(y - {y_1}) = m(x - {x_1})$ or $y - 0 = \frac{4}{3}(x - 0)$ or $3y = 4x$ or $4x - 3y = 0$.

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