Slope-Intercept Form of a Line
y = mx + b
Where the slope is given by:
m = (y2 - y1)/(x2 - x1) m = rise/run
Distance Formula
The distance between two points (x1,y1) and (x2,y2) is found by using the Pythagorean Theorem:
D = sqrt((x2-x1)^2 + (y2-y1)^2)
Midpoint of a Line
The midpoint, M, of a line segment (x1,y1) to (x2,y2) is given by:
M = (x,y) = ((x1+x2/2), (y1+y2)/2)
Test for Perpendicular Lines
Two lines with slopes M1 and M2 are perpendicular if:
M1 = -1/M2
the cosine of the angle between them is 0
Parametric Form of a Line
Given points P1 = (x1,y1) and P2 = (x2,y2), the parametric form for a line is:
x = x1 + t(x2-x1) y = y1 + t(y2-y1) 0 <= t <= 1t is called the parameter. When t = 0 we get P1 and when t = 1 we get P2. As t varies between 0 and 1, we get all the other points on the line segment between P1 and P2.
Equation for a Circle The equation for a of radius r centered at (0,0):
x^2 + y^2 = r^2 y = +/- sqrt(r^2 - x^2) -r <= x <= r
Polar Form of a Circle
x = r cos(theta) y = r sin(theta) 0 <= theta <= 360 degrees
Convex Polygons
Triangles
For a triangle with angles A,B,C and opposite sides a,b,c:
A + B + C = 180 degrees sin(A)/a = sin(B)/b = sin(C)/c c^2 = a^2 + b^2 - 2ab*cos(C)Note: When C = 90 degrees in the third equation, it boils down to the Pythagorean Theorem.
