A-Level Maths | Co-ordinate Geometry

Gradient
- find two co-oordinates on the line
- change in y/ change in x
Midpoint between two points
- (mean of x-coordinates, mean of y-coordinates)
Gradient of a parallel line
- same
Gradient of a perpendicular line
- negative reciprocal
Distance between two co-ordinates
- pythagoras
- length² = width² + height²
- l² = (x₂- x₁)² + (y₂ - y₁)²
Equation of a line
- y = mx + c
- to find c: substitute x and y from a point on the line
- y - y1 = m(x - x1)
Intersection between two lines
- solve them simultaneously
- substitute one equation into the other
Equation of a circle
Equation of a tangent to a circle
- find the gradient from the centre to the point (radius)
- tangent is perpendicular to radius
- y = mx + c