IB Maths AI SL 3.5 Notes – Equations of Perpendicular Bisectors

This IB Maths AI SL 3.5 resource introduces the equations of perpendicular bisectors and is fully aligned with the IB Applications and Interpretation SL syllabus.

Students learn how to determine the equation of a line that bisects a segment at a right angle by combining coordinate geometry concepts such as midpoints, gradients, and point–slope form. The notes explain how a perpendicular bisector passes through the midpoint of a line segment and has a gradient that is the negative reciprocal of the original line’s gradient.

The resource develops a clear step-by-step method: finding the midpoint of two coordinates, calculating the gradient of the original segment, determining the perpendicular gradient, and forming the equation of the new line.

Worked examples and contextual practice problems help students apply perpendicular bisectors to real situations, such as determining boundaries where points are equidistant from two locations and solving geometric problems involving coordinates.

Ideal for IB Maths AI SL teachers teaching coordinate geometry, gradients of perpendicular lines, and geometric loci using perpendicular bisectors.