IB Maths AI 3.5 Definitions

This page contains our IB Maths AI definitions for 3.5. By learning each one of these definitions, you will fully cover the content for IB Maths AI 'Perpendicular bisectors'.

All Topic 3 Sub-topics 3.1: Fundamentals Of Geometry 3.2: Introduction To Trigonometry 3.3: Applied Trigonometry 3.4: Circles 3.5: Perpendicular Bisectors 3.6: Voronoi Diagrams (HL)3.7: Unit circle (HL)3.8: Geometric transformations (HL)3.9: Vectors (HL)3.10: Vector lines (HL)3.11: Graph theory (HL)3.12: Adjacency matrices (HL)3.13: Algorithms & problems

bisector

A line that divides a line segment into two equal parts by passing through its midpoint.

gradient

The coefficient

a

y=ax+b

, giving the predicted change in

y

when

x

increases by

1

midpoint

The point halfway along the line segment joining two points; for $A\left(x_1,y_1,z_1\right)$ and $B\left(x_2,y_2,z_2\right)$ it is $M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2},\frac{z_1+z_2}{2}\right)$ .

negative reciprocal

The value obtained by changing the sign and inverting a non-zero number; for a gradient

m

, the perpendicular gradient is

-\frac{1}{m}

perpendicular

Meeting at a right angle, so the angle between the two lines is

90^{\circ}

perpendicular bisector

A line that passes through the midpoint of a line segment and is perpendicular to the segment.

point-gradient

A form of a straight-line equation using a point

(x_1,y_1)

and gradient

m

y-y_1=m\left(x-x_1\right)

vertical

Describing changes parallel to the

y

-axis, such as a stretch by factor

|a|

or a shift up or down by

d

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