Line segments (Edexcel GCSE Maths): Revision Notes

Line segments

What is a line segment?

A line segment is a straight line section that connects two specific points. Unlike a full line that continues infinitely in both directions, a line segment has definite start and end points. When working with coordinate geometry, you can calculate the exact length of any line segment if you know the coordinates of both endpoints.

Finding the length of a line segment

To find the length of a line segment when you have coordinate points, you need to use Pythagoras' theorem. This method works by creating a right-angled triangle where the line segment becomes the hypotenuse.

The mathematical formula for finding the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Step-by-step method

The process involves creating a right-angled triangle and applying mathematical principles to find the exact distance between two coordinate points.

Step 1: Identify your two coordinate points

• Label your points clearly (e.g., Point A and Point B)

Step 2: Calculate the horizontal distance

• Subtract the x-coordinates: larger x-value minus smaller x-value
• This gives you one side of your right-angled triangle

Step 3: Calculate the vertical distance

• Subtract the y-coordinates: larger y-value minus smaller y-value
• This gives you the other side of your right-angled triangle

Step 4: Apply Pythagoras' theorem

• Use the formula: $(line\ segment)^2 = (horizontal\ distance)^2 + (vertical\ distance)^2$
• Calculate the square root to find the actual length

Step 5: Round your answer appropriately

• Usually to 2 decimal places for exam questions

Working with negative coordinates

When dealing with coordinate problems, negative coordinates often cause confusion and calculation errors. The key principle to remember is that when subtracting a negative number, it's the same as adding a positive number.

The line segment always forms the hypotenuse of your right-angled triangle, and you can only substitute positive values into Pythagoras' theorem. This is why we calculate the absolute differences between coordinates.

Key points to remember

• The line segment always forms the hypotenuse of your right-angled triangle
• You can only substitute positive values into Pythagoras' theorem
• When coordinates are negative, pay close attention to your subtraction
• Always check your final answer makes sense - distances cannot be negative

Exam tips

Success in coordinate geometry questions requires careful method and attention to detail. Here are the most important strategies to help you avoid common pitfalls and maximise your marks:

Remember that examiners award method marks even when your final answer is incorrect, so clear working is essential for maximising your score.