Coordinate Geometry

Centroid

Where three medians of a triangle intersect

Circumcentre

Where three mediators of a triangle intersect

Orthocentre

Where three lines from each vertex perpendicular to its opposite side intersect

Median of a triangle

Line which joins a vertex of a triangle to the midpoint of its opposite side

Mediator

Perpendicular bisectors of the sides of a triangle

When two lines are perpendicular, what is the product of their slopes?

m₁ x m₂ = -1

When are modulus signs not used when using the perpendicular distance equation?

When you require a positive or a negative answer, eg. finding where points lie on a plane

Collinear

All points are in the same line, ie same slope

Equation of a circle w a centre at (0,0)

x² + y² = r² (r = radius)

How to show that a line is a tangent to a circle

Distance from the centre to the line should equal the radius

To find intersection of two circles (ie common chord or tangent)

1. Find equation of common chord by taking s₁ from s₂, as s₁ - s₂ = 0

2. Find points of intersection of chord and any one of circles

Finding the distance of radii when touch externally and internally

• Externally: d = r₁ + r₂

• Internally: d = r₁ - r₂

When a circle touches the x- or y-axis when finding it’s radius

The radius of the circle is equal to one of the coordinates of its centre, ie |-f| or |-g|

√g² + f² - c = |-f|

g² + f² - c = f²

g² = c and vice versa

When finding the equation of tanget that touches two given circles

Simultaneous equations to isolate x and y