The length intercepted by the straight line `12 x - 9y = 108` between the corrdinate axes is

Options

A. 12 unit
B. 18 unit
C. 15 unit
D. 9 unit

Answer

To find the length intercepted by the straight line \( 12x - 9y = 108 \) between the coordinate axes, we will follow these steps:

### Step 1: Find the x-intercept
To find the x-intercept, we set \( y = 0 \) in the equation.

\[ 12x - 9(0) = 108 \implies 12x = 108 \implies x = \frac{108}{12} = 9 \]

Thus, the x-intercept is \( (9, 0) \).

### Step 2: Find the y-intercept
Next, we find the y-intercept by setting \( x = 0 \) in the equation.

\[ 12(0) - 9y = 108 \implies -9y = 108 \implies y = \frac{108}{-9} = -12 \]

Thus, the y-intercept is \( (0, -12) \).

### Step 3: Calculate the distance between the intercepts
The intercepts we found are \( A(9, 0) \) and \( B(0, -12) \). To find the distance \( AB \), we can use the distance formula:

\[ AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Substituting the coordinates of points A and B:

\[ AB = \sqrt{(0 - 9)^2 + (-12 - 0)^2} = \sqrt{(-9)^2 + (-12)^2} = \sqrt{81 + 144} = \sqrt{225} = 15 \]

### Conclusion
The length intercepted by the straight line \( 12x - 9y = 108 \) between the coordinate axes is \( 15 \) units.

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