Page 2: Reduced Equations and Relative Positions

This section explores the reduced forms of équation cartésienne d'une droite and introduces the concept of relative positions between lines. The slope-intercept form y = mx + p is thoroughly explained.

Definition: The slope-intercept form y = mx + p represents a line where m is the slope and p is the y-intercept.

Example: The slope between two points A and B is calculated using m = (yB - yA)/(xB - xA).

Highlight: Two lines are parallel if and only if they have collinear direction vectors or equal slopes.

Page 3: Line Positions and Intersections

This page details the various positions of lines in a plane, focusing on parallel and intersecting cases. The content builds upon the position relative de deux droites dans le plan concept.

Definition: Lines are intersecting if their slopes are different (m ≠ m').

Example: When two lines intersect, their point of intersection can be found by solving their equations simultaneously.

Highlight: The relative position of lines can be determined by comparing their slopes and y-intercepts.

Page 4: Circle Equations

The final page introduces circle equations and distance calculations in Géométrie repérée. The standard form of a circle equation is presented with its center and radius parameters.

Definition: The equation of a circle with center A(x₁,y₁) and radius R is $x-x₁$² + $y-y₁$² = R².

Example: The distance between two points A and B is calculated using the formula √[(xB-xA)² + (yB-yA)²].

Highlight: The radius of a circle can be determined by calculating the distance between any two points on its circumference.

Page 1: Cartesian Equations of Lines

This page introduces the fundamental concepts of équation cartésienne d'une droite and associated vectors. The general form of a line's Cartesian equation is presented as ax + by + c = 0, accompanied by explanations of directional and normal vectors.

Definition: A Cartesian equation of a line takes the form ax + by + c = 0, where a, b, and c are constants.

Vocabulary: A directional vector is any non-zero vector parallel to the line's direction.

Example: For a line parallel to the y-axis, the equation takes the simplified form x = n.

Highlight: The normal vector to a line is perpendicular to any directional vector of that line, typically represented as v(a,b).