O Level MathematicsC3.1 Coordinates (use Cartesian coordinates).

📍 Plot Your Success with Coordinates!

Edudent Academy
26 Dec 25

Understanding **Cartesian coordinates** is the gateway to graphing straight lines, interpreting maps, and even programming video games! Mastering this topic will help you tackle exam questions swiftly and build a solid foundation for higher-level mathematics.

What Are Cartesian Coordinates?

A point in the plane is written as
(x, y)(x,\,y)
where **xx** measures the horizontal distance from the origin and **yy** measures the vertical distance. The plane is divided into four quadrants, and every point tells its own positional story.

  • Quadrant I: (+,+)(+,+) — both xx and yy positive.
  • Quadrant II: (−,+)(-,+) — xx negative, yy positive.
  • Quadrant III: (−,−)(-,-) — both negative.
  • Quadrant IV: (+,−)(+,-) — xx positive, yy negative.

Worked Example: Finding a Midpoint

Problem: The points A(2, 3)A(2,\,3) and B(8, −5)B(8,\,-5) form a line segment. Find the midpoint MM of ABAB.

  • Step 1: Use the midpoint formula
    M(x1+x22,  y1+y22).M\left(\frac{x_1+x_2}{2},\;\frac{y_1+y_2}{2}\right).
  • Step 2: Substitute
    x1=2,  x2=8,  y1=3,  y2=−5.x_1=2,\;x_2=8,\;y_1=3,\;y_2=-5.
  • Step 3:
    M(2+82,  3+(−5)2)=M(5, −1).M\left(\frac{2+8}{2},\;\frac{3+(-5)}{2}\right)=M(5,\,-1).

The midpoint is (5, −1)(5,\,-1). **Practise** plotting points, finding distances, and midpoints daily to gain confidence for your O Level exam!