Final answer:
The correct method to find the distance from the point (3,8) to the line y=1/5x-3, is to use the formula derived from the Pythagorean theorem for the perpendicular distance from a point to a line.
Step-by-step explanation:
To find the distance from the point (3,8) to the line y=1/5x-3, we use the formula for the perpendicular distance from a point to a line, which is derived from the Pythagorean theorem. First, we write the equation of the line in its general form Ax + By + C = 0. For y = (1/5)x - 3, we can rewrite it as -(1/5)x + y + 3 = 0.
Next, we apply the distance formula: Distance = |Ax + By + C| / √(A² + B²), where (x, y) is the point. Plugging in the values: Distance = |-1/5(3) + 8 + 3| / √((-1/5)² + 1²) = |(1/5)(-3) + 11| / √(1/25 + 1) = |-0.6 + 11| / √(26/25) = 10.4 / √(1.04) = 10.4 / 1.02, which simplifies to approximately 10.2.
This calculation provides the shortest distance between the point and the line, not the distance between two points or the use of a midpoint formula, but the distance along the perpendicular line from the point to the given line.