Question : The length of the intercept of the graph of the equation $9x-12y=108$ between the two axes is:
Option 1: 15 units
Option 2: 9 units
Option 3: 12 units
Option 4: 18 units
Correct Answer: 15 units
Solution :
Given: The graph of the equation is $9x–12y=108$.
Substitute $x=0$ in the above equation, we get,
$9\times0 -12y=108$
⇒ $–12y=108$
⇒ $y=–9$
Substitute $y=0$ in the equation $9x-12y=108$, we get,
$9x-12\times0=108$
⇒ $9x=108$
⇒ $x=12$
Using Pythagoras theorem in $\triangle BOA$, we get,
$AB^2= OA^2+OB^2$
⇒ $AB=\sqrt{OA^2+OB^2}$
⇒ $AB=\sqrt{12^2+9^2}=\sqrt{144+81}$
⇒ $AB=\sqrt{225}=15$ units
Hence, the correct answer is 15 units.
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