Two-dimensional coordinate geometry is a combination of algebra and geometry. A systematic study of geometry by the use of algebra was first carried out by celebrated French philosopher and mathematician René Descartes, in his book ‘La Géométry, published in 1637.
This book introduced the notion of the equation of a curve and related analytical methods into the study of geometry. The resulting combination of analysis and geometry is referred now as analytical geometry.
If a line makes an angle α with the positive direction of x-axis, then the slope of the line is given by m = tan α, α ≠ 90°. Slope of horizontal line is zero and slope of vertical line is undefined.
Two lines are parallel if and only if their slopes are equal. Two lines are perpendicular if and only if product of their slopes is -1. Three points A, B and C are collinear, if and only if slope of AB = slope of BC.
Equation of the horizontal line having distance a from the x-axis is either y = a or y = -a. Equation of the vertical line having distance b from the y-axis is either x = b or x = -b.
The point (x, y) on the line with slope m and y-intercept c lies on the line if and only if y = mx + c.
Any equation of the form Ax + By + C = 0, with A and B are not zero, simultaneously, is called the general linear equation or general equation of a line.