Formulas and Definitions Flashcards
Distance Formula
◇x=/(x2-x1)² + (y2-y1)²
Midpoint Formula
M[ (x1+x2)/2 ; (y1+y2)/2 ]
Gradient Formula
m=◇y/◇x
Straight Line Equation
y=mx+c
If the gradient of two lines are equal…
The lines are parallel
If two lines are perpendicular…
Then the products of their gradients will be -1.
Collinear points…
Lie on the same line.
Median
A line from the vertex of a triangle to the midpoint of the opposite side.
Altitude/height/perpendicular height
A line from the vertex of a triangle, perpendicular to the opposite side.
Perpendicular bisector
This passes through the midpoint of the line and is perpendicular to that line.
The Equation of a Circle centre at the origin.
x²+y²=r²
The Equation of a Circle non centered at the origin.
(x-a)²+(y-b)²=r²
(a;b) 》the centre coordinates
A quadrilateral made up of two tangents from the same point and the two radii to the points of contact is a kite, therefore…
(2 pairs adj sides =)
By the properties of a kite the diagonals are perpendicular and the diagonal between the two equal sides bisect the other diagonal.
Tangents
Perpendicular to Radius.
Any two tangents drawn to a circle from the same external point will be equal in length.
Amplitude Formula
(max value-min value)/2
