Summary
Coordinate geometry involves understanding the properties and equations of lines on a graph. It includes concepts such as gradients, mid-points, and the relationships between perpendicular and parallel lines.
- Gradient — the steepness of a line, calculated as the change in y divided by the change in x. Example: For the line y = 2x + 3, the gradient is 2.
- Mid-Point — the point that is exactly halfway between two points on a line. Example: The mid-point of (2, 3) and (4, 7) is (3, 5).
- Perpendicular Lines — lines that intersect at a right angle, with gradients that are negative reciprocals. Example: If one line has a gradient of 2, a perpendicular line will have a gradient of -1/2.
- Parallel Lines — lines that never intersect, having the same gradient. Example: Lines y = 3x + 1 and y = 3x - 4 are parallel.
Exam Tips
Key Definitions to Remember
- Gradient is the change in y over the change in x.
- Mid-point is the average of the x-coordinates and y-coordinates of two points.
- Perpendicular lines have gradients that are negative reciprocals.
- Parallel lines have the same gradient.
Common Confusions
- Confusing the formula for gradient with the formula for mid-point.
- Forgetting that perpendicular gradients are negative reciprocals, not just negatives.
Typical Exam Questions
- What is the gradient of the line y = 5x + 2? Answer: 5
- What are the coordinates of the mid-point between (1, 2) and (3, 4)? Answer: (2, 3)
- What is the equation of a line parallel to y = 2x + 3 that passes through (0, 1)? Answer: y = 2x + 1
What Examiners Usually Test
- Ability to calculate and interpret the gradient of a line.
- Understanding of how to find mid-points between two coordinates.
- Knowledge of the properties of perpendicular and parallel lines.