Final answer:
The perpendicular distance of the point (4, -3) from the line 3x - 4y - 1 = 0 is calculated using the distance formula and is found to be 4.6 units.
Step-by-step explanation:
To calculate the perpendicular distance of a point from a line, we use the formula derived from the equation of the line:
d = |Ax1 + By1 + C| / √(A² + B²),
where d is the perpendicular distance, (x1, y1) is the point, and Ax + By + C = 0 is the equation of the line. For the point (4, -3) and the line equation 3x - 4y - 1 = 0, the formula becomes:
d = |(3)(4) + (-4)(-3) - 1| / √(3² + (-4)²),
which simplifies to:
d = |12 + 12 - 1| / √(9 + 16),
d = 23 / √25,
d = 23 / 5,
d = 4.6.
Therefore, the perpendicular distance of the point (4, -3) from the line 3x - 4y - 1 = 0 is 4.6 units.