The equation of a line is `3x - 4y + 12 = 0`. It meets the x-axis at point A and the y-axis at point B. Find :
the co-ordinates of points A and B.

Answer

To find the coordinates of points A and B where the line given by the equation \(3x - 4y + 12 = 0\) meets the x-axis and y-axis respectively, we can follow these steps:

### Step 1: Identify the x-intercept (Point A)
To find the x-intercept, we set \(y = 0\) in the equation of the line.

\[ 3x - 4(0) + 12 = 0 \]

This simplifies to:

\[ 3x + 12 = 0 \]

Now, solve for \(x\):

\[ 3x = -12 \]
\[ x = -4 \]

Thus, the coordinates of point A are:

\[ A(-4, 0) \]

### Step 2: Identify the y-intercept (Point B)
To find the y-intercept, we set \(x = 0\) in the equation of the line.

\[ 3(0) - 4y + 12 = 0 \]

This simplifies to:

\[ -4y + 12 = 0 \]

Now, solve for \(y\):

\[ -4y = -12 \]
\[ y = 3 \]

Thus, the coordinates of point B are:

\[ B(0, 3) \]

### Final Answer
The coordinates of points A and B are:
- A: \((-4, 0)\)
- B: \((0, 3)\)

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