Example 1: Plotting Points
Plot the points A(3, -2), B(-1, 4), and C(-2, -3)
Solution:
- A(3, -2): Go 3 units right, 2 units down → Quadrant 4
- B(-1, 4): Go 1 unit left, 4 units up → Quadrant 2
- C(-2, -3): Go 2 units left, 3 units down → Quadrant 3
Example 2: Distance Between Points
Find the distance between A(1, 2) and B(4, 6)
Solution:
Using the distance formula:
Distance = √[(4 - 1)² + (6 - 2)²]
= √[3² + 4²]
= √[9 + 16]
= √25 = 5 units
Example 3: Finding the Midpoint
Find the midpoint of the line segment joining P(-3, 1) and Q(5, -3)
Solution:
Using the midpoint formula:
Midpoint = ((-3 + 5)/2, (1 + (-3))/2)
= (2/2, -2/2)
= (1, -1)
This deep dive covers Worked Examples within Coordinates for GCSE Mathematics. Revise Coordinates in Graphs for GCSE Mathematics with 10 exam-style questions and 20 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 7 of 8 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Coordinates
Which point has coordinates (–3, 5)?
A triangle has vertices at P(−1, 2), Q(3, 5) and R(7, 2). Show that the triangle is isosceles.