Slope and Distance to a Line
This page delves deeper into finding the slope (coefficiente angolare) of a line and introduces the concept of distance from a point to a line.
The slope formula is revisited:
m = (y₂ - y₁) / (x₂ - x₁)
Examples are provided for calculating slope given two points.
The point-slope form of a line equation is emphasized:
y - y₁ = m(x - x₁)
The page concludes with the formula for the distance from a point to a line:
d = |ax₀ + by₀ + c| / √(a² + b²)
Where (x₀, y₀) is the point and ax + by + c = 0 is the equation of the line in implicit form.
Definition: The coefficiente angolare (slope) of a line measures its steepness and direction, represented by m in the equation y = mx + q.
Example: For a line passing through A(2,-3) and B(-1,4), the slope is calculated as m = (4 - (-3)) / (-1 - 2) = 7 / -3 = -7/3.
Highlight: Understanding slope is crucial for analyzing the relationship between lines, including parallel and perpendicular lines.
Vocabulary: The distance from a point to a line is the length of the perpendicular segment from the point to the line.