I would like to coin together certain properties of

I would like to coin together certain properties of Coordinate Geometry (from the basics) that I learnt from various sources, some even from the forum. Would appreciate your help in adding more or correcting these.

SLOPE:

slope m=(y1-y2)/(x1-x2)

*A straight line with a -ve slope passes through II and IV quadrants
A straight line with a +ve slope passes through I and III quadrants

*If the slope is 1 the angle formed by the line is 45 degrees

*If the slope of a line is n, the slope of a line perpendicular to it is its -ve reciprocal, -1/n

*If a line is horizontal, slope=0, equation is y=b

*If a line is vertical, slope is not defined, equation is x=a, where a is x-intercept.

*Parallel lines have same slope.

EQUATION:

Equation of a circle is (x - a)^2 + (y-b)^2 = r^2, where (a,b) is the center and r is the radius

Equation of a circle is x^2+y^2=r^2 if (0,0) is the center

Equation of a line is y=mx+b, where m=slope and b=y intercept

* y intercept is the value of y when x is 0
x intercept is the value of x when y is 0

* Points that solve the equation of a line are in the same line

*Given a point and slope, equation of the line can be found

*Given the equation, x and y intercepts can be found


DISTANCE between two points = sqrt[(x1-x2)^2+(y1-y2)^2]

MIDPOINT: xm=(x1+x2)/2 ym=(y1+y2)/2

I know, the properties do not end here. Hope you guys join in.