What is the distance from the point (2, -3) to the line 3x + 4y - 12 = 0?

What is the distance from the point (2, -3) to the line 3x + 4y - 12 = 0?

Step 1: Identify the point and the line. The point is (2, -3) and the line is given by the equation 3x + 4y - 12 = 0.
Step 2: Rewrite the line equation in the form Ax + By + C = 0. Here, A = 3, B = 4, and C = -12.
Step 3: Use the distance formula from a point (x0, y0) to a line Ax + By + C = 0, which is: Distance = |Ax0 + By0 + C| / √(A² + B²).
Step 4: Substitute the values into the formula. Here, x0 = 2 and y0 = -3.
Step 5: Calculate Ax0 + By0 + C: 3*2 + 4*(-3) - 12 = 6 - 12 - 12 = -18.
Step 6: Take the absolute value: |-18| = 18.
Step 7: Calculate √(A² + B²): √(3² + 4²) = √(9 + 16) = √25 = 5.
Step 8: Divide the absolute value by the square root: Distance = 18 / 5 = 3.6.

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