A) \[y=4\]
B) \[4x-3y+8=0\]
C) \[4x-3y=0\]
D) \[4x-3y+6=0\]
Correct Answer: C
Solution :
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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