Straight Lines — Class 11 Mathematics

Coordinate geometry represents the straight line algebraically, building on the distance, section and area formulae from earlier classes. The inclination of a line gives its slope , and for two points the slope is . Two lines are parallel iff their slopes are equal and perpendicular iff ; the acute angle between them satisfies . The chapter derives several forms of a line's equation: point-slope , two-point, slope-intercept , intercept , and the general form . The distance of a point from the line is , and the distance between parallel lines and is . Special cases include horizontal lines and vertical lines , while three points are collinear iff the slope of equals the slope of (equivalently, the area of triangle is zero). Any first-degree equation , with not both zero, represents a straight line and can be reduced to any of these standard forms. These tools handle collinearity, concurrency of lines, reflections of a point in a line, and many geometric and real-life applications such as relating two linearly varying quantities.