Coordinate Geometry Formulas

Coordinate Geometry Formulas for O-Level

These coordinate geometry formulas are part of the Additional Math & Math O-Level syllabus in Singapore.

Gradient (Slope) of a Line

Formula:

$$m = \frac{y_2 – y_1}{x_2 – x_1}$$

This tells you how steep a line is.

Equation of a Straight Line

Formula:

$$y – y_1 = m(x – x_1) \quad \text{or} \quad y = mx + c$$

Use this to write the equation of a line when you know a point and the gradient.

Mid-point of a Line

Formula:

$$\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$

This gives you the point exactly halfway between two points.

Note: This mid-point formula is only required in Additional Math.

Distance Between Two Points

Formula:

$$\sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}$$

This calculates the straight-line distance between two points.

Parallel Lines

If two lines are parallel, they have the same gradient.

➕ Perpendicular Lines

If two lines are perpendicular (meet at 90°), their gradients multiply to -1.

Formula:

$$m_1 \times m_2 = -1 \quad \text{or} \quad m_1 = -\frac{1}{m_2}$$

Note: This perpendicular gradient formula is only required in Additional Math.

Area of Triangle / Polygon (Shoelace Formula)

This formula helps you find the area of a triangle or polygon using coordinates. (Click the attached file on the right)

Note: The shoelace area formula is only taught in Additional Math.

These formulas are essential for solving coordinate geometry questions in exams. If you’re taking Additional Math, make sure you’re familiar with all of them!

coordinate geometry formulas for additional math (a-math) and math. n-level and o-level . best tutor/tuition in woodlands and boon lay