Coordinate Geometry IGCSE
Coordinate Geometry
Gradient (Slope) of a Straight Line
The gradient of a straight line is defined as the ratio of the vertical change to the horizontal change between two points on the line.
For two points A(x₁, y₁) and B(x₂, y₂) on a line, the gradient is calculated as:
gradient of AB = (y₂ - y1) / (x₂ - x1)Length of a Line Segment
The length of a line segment PQ between two points (x₁, y₁) and (x₂, y₂) is given by:
PQ = √[(x₂ - x1)² + (y₂ - y1)²]Equations of Straight Lines
| Form | Data Required | Equation |
|---|---|---|
| Slope-point form | Slope m, one point (x₁, y₁) | y - y₁ = m(x - x₁) |
| Two-point form | Two points (x₁, y₁) and (x₂, y₂) | (y - y₁) / (y2 - y1) = (x - x₁) / (x2 - x1) |
| Slope-intercept form | Slope m, y-intercept c | y = mx + c |
| Two-intercept form | x-intercept a, y-intercept b | x/a + y/b = 1 |
Special Cases
- Horizontal Line: Parallel to x-axis, equation: y = c (constant)
- Vertical Line: Parallel to y-axis, equation: x = a (constant)
Note: The gradient of a horizontal line is 0, while the gradient of a vertical line is undefined.
Quiz 1
Quiz 2
