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ANALITIC GEOMETRY, x-a=0 since md=(y-b)/(x-a) is not defined, image, image…
ANALITIC GEOMETRY
SLOPE
Positive Slope
Slope Equation
y = mx + b
If the lines passing through the origin
y=mx
Slope of a Line passing Through Two Points
formula
m=(y2-y1)/(x2-x1)
The Slope of the Line passing through the origin is
formula
m=y/x
Collinear Points have same Slopes
mAB=mAC=mBC
LINE EQUATIONS
Equation of Line in Slope - Point form
y-y1=m.(x-x1)
EQUATION OF A LINE IN TWO POINT FORM
⇒ m = (y2 – y1)/(x2 – x1)
y2 – y1 = m(x2 – x1)
y – y1 = {(y2 – y1)/(x2 – x1)}(x – x1)
STANDART EQUATION OF A LINE
ax+by+c=0
EQUATION OF A LINE WITH KNOWN INTERCEPTS ON THE AXES
x/a+y/b=1
RELATIVE POSITIONS
Intersecting lines
if they have on point in common
Coincident lines
if they have all points in common
Parallel lines
if they have no points in common
EQUATION OF A LINE PARALLEL TO X/Y AXIS
for x axis
md=0 0=(y-b)/(x-a)
y-b=0 y=b
for y axis
md is not defined since tan90 is not defined
MIDPOINT
formula
(x3, x3)= [(x1+x2)/2, (y1+y2)/2]
DISTANCE BETWEEN TWO POINTS FORMULA
d = √[(x2−x1)2+(y2−y1)2]
x-a=0 since md=(y-b)/(x-a) is not defined
x=a
