Vector Coordinates and Line Equations
This page introduces fundamental concepts related to współrzędne wektora (vector coordinates) and line equations in a coordinate system.
The formula for vector coordinates is presented as AB = [x₂ - x₁, y₂ - y₁]. This allows for calculating the horizontal and vertical components of a vector between two points.
Definition: The długość wektora wzór (vector length formula) is given by |AB| = √((x₂ - x₁)² + (y₂ - y₁)²), which calculates the straight-line distance between two points.
For finding the midpoint of a line segment, the formula (x₁ + x₂)/2, (y₁ + y₂)/2 is provided. This is useful for various geometric calculations.
The page also covers the slope formula, expressed as a = (y₂ - y₁)/(x₂ - x₁) = tan α. This is crucial for understanding the inclination of lines in the coordinate system.
Example: For parallel lines, y = a₁x + b₁ || y = a₂x + b₂, the condition a₁ = a₂ must be satisfied.
Highlight: Perpendicular lines have a special relationship between their slopes: a₁a₂ = -1 (or a₂ = -1/a₁).
The page concludes with examples of perpendicular lines, such as y = √3x + 3 ⊥ y = -2x - 6 and y = -7x + 1 ⊥ y = 1/7x - √3, demonstrating the application of the perpendicularity condition.