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

Answer

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

### Step 1: Find the coordinates of point A (where the line meets the x-axis)
At the x-axis, the value of \(y\) is always \(0\). Therefore, we can substitute \(y = 0\) into the equation of the line.

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

This simplifies to:

\[ 3x + 12 = 0 \]

### Step 2: Solve for \(x\)
Now, we can isolate \(x\):

\[ 3x = -12 \]
\[ x = \frac{-12}{3} = -4 \]

Thus, the coordinates of point A are:

\[ A(-4, 0) \]

### Step 3: Find the coordinates of point B (where the line meets the y-axis)
At the y-axis, the value of \(x\) is always \(0\). Therefore, we can substitute \(x = 0\) into the equation of the line.

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

This simplifies to:

\[ -4y + 12 = 0 \]

### Step 4: Solve for \(y\)
Now, we can isolate \(y\):

\[ -4y = -12 \]
\[ y = \frac{-12}{-4} = 3 \]

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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