Summary
In coordinate geometry, you learn to calculate the gradient of a line, find the midpoint of a line segment, and determine the distance between two points.
- Gradient — the measure of a line's steepness, calculated by dividing the change in the y-coordinate by the change in the x-coordinate. Example: For line AB with points A(2, 7) and B(5, 1), the gradient is (1 - 7) / (5 - 2) = -2.
- Midpoint — the point exactly halfway between two points on a line segment. Example: The midpoint of AB with points A(2, 7) and B(5, 1) is ((2 + 5)/2, (7 + 1)/2) = (3.5, 4).
- Distance — the length of a line segment between two points, calculated using Pythagoras' theorem. Example: The distance between A(3, 4) and B(5, 8) is √((5-3)² + (8-4)²) = √20.
Exam Tips
Key Definitions to Remember
- Gradient is the change in y divided by the change in x.
- Midpoint is the average of the x-coordinates and y-coordinates of two points.
- Distance is calculated using Pythagoras' theorem.
Common Confusions
- Mixing up the formula for gradient with the formula for distance.
- Forgetting to divide by 2 when calculating the midpoint.
Typical Exam Questions
- What is the gradient of the line y = -3x + 4? Answer: -3
- Find the midpoint of the line segment joining (2, 8) and (6, 0). Answer: (4, 4)
- Calculate the distance between points (3, 4) and (5, 8). Answer: √20
What Examiners Usually Test
- Ability to calculate the gradient from two points.
- Finding the midpoint of a line segment.
- Using Pythagoras' theorem to find the distance between two points.