IB MATHEMATICS AA · TOPIC 2.1 · TOPIC 2 BUNDLE
A complete foundation chapter for IB Mathematics AA, now included in the €50 Topic 2 Functions bundle. Learn how gradients describe direction, how equations encode straight lines, why perpendicular gradients multiply to −1, how perpendicular bisectors are constructed, and how exact algebra and GDC methods fit together.
WHAT YOU NEED TO KNOW
Students often memorise formulas for gradient and line equations without seeing the picture behind them. This chapter starts with the geometry first. A gradient tells us how quickly a line rises or falls. A midpoint gives the centre of a segment. A perpendicular bisector combines both ideas: first find the midpoint, then turn the direction through 90°. Once those ideas are secure, the algebra becomes much more natural.
For two points \(A(x_1,y_1)\) and \(B(x_2,y_2)\), gradient compares vertical change with horizontal change. Positive means rising, negative means falling, zero means horizontal, and a vertical line has undefined gradient.
If you know a point and a gradient, \(y-y_1=m(x-x_1)\) is usually the cleanest start. If you need an intercept quickly, \(y=mx+c\) is often more useful. The notes explain when each form saves time.
For non-vertical perpendicular lines, \(m_1m_2=-1\). The chapter uses true right-angle sketches so the algebra matches the geometry students are meant to visualise.
You will solve intersections by substitution or elimination and then see the equivalent graphing route on both the Casio fx-CG50 and TI-Nspire CX II.
MINI WORKED EXAMPLE
Suppose line \(L_1\) passes through \(A(-2,-1)\) and \(B(4,3)\). First calculate its gradient:
A perpendicular line therefore has gradient \(-\frac{3}{2}\). If the second line also passes through \(A(-2,-1)\), use point-gradient form:
The important idea is the order: find the original direction → rotate it by 90° → anchor the new line through the required point.
Lines & Coordinate Geometry is now part of the complete Topic 2 bundle rather than a separate free chapter. The €50 Topic 2 purchase unlocks Lines, Quadratics, Composition & Inverse Functions, Exponentials & Logarithms, and Asymptotes & Rational Functions in My Notes.
Open the complete Topic 2 bundle →CONTINUE TOPIC 2
The next chapter develops graph shape, roots, discriminants, Vieta's formulae, inequalities, optimisation and parameter problems.