Question

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

• A. $y = 4$
• B. $4 x - 3 y + 8 = 0$
• C. $4 x - 3 y = 0$
• D. $4 x - 3 y + 6 = 0$

Answer 1

Answer: (C)

$4 x - 3 y = 0$

Answer 2

Given, line AB making 0 intercepts on x-axis and y-axis or $\left( x _ { 1 } , y _ { 1 } \right) \equiv ( 0,0 )$ and the line is perpendicular to line $C D , 3 x + 4 y + 6 = 0$ . We know that standard equation of a line is $y = a x + b$ 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

$C D = - \frac { a } { b } = \frac { - 3 } { 4 }$ Since the line AB is perpendicular to the line CD, therefore slope of the line $A B ( m ) = \frac { 4 } { 3 }$. Thus relation for the equation of the line AB will be $\left( y - y _ { 1 } \right) = m \left( x - x _ { 1 } \right)$ or $y - 0 = \frac { 4 } { 3 } ( x - 0 )$ or $3 y = 4 x$ or $4 x - 3 y = 0$.