Slope and Distance to a Line
This page delves deeper into finding the slope coefficienteangolare 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 = mx−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 A2,−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.