ANGLE BETWEEN TWO LINES
-Let consider 
and 
where Q is angle made between 
and 
and 
is the angle of 
and 
is the angle of 
.
-Consider the figure below
Our intentions to find the value of 
which always should be acute angle.
where
PARALLEL AND PERPENDICULAR LINES
(a) PARALLEL LINES
-Are the lines which never meet when they are produced
Means that 
is parallel to 
symbolically 
//
– -However condition for two or more lines to be parallel state that they posses the same gradient.
b) PERPENDICULAR LINES
– -Are the lines which intersect at right angle when they are produced.
Means that 
is perpendicular to 
– -Symbolically is denoted as L1⊥L2
– -However the condition for two or more lines to be perpendicular states that “The product of their slopes should be equal to negative one”.
– -Let consider the figure below
NOTE:
1. The equation of the line parallel to the line 
= 0 passing through a certain point is of the form of 
. Where 
– is constant.
2. The equation of the line perpendicular to the line 
pass through a certain point is of the form of 
when 
– is constant.
3. The calculation of K above done by substitution certain point passing through.
THE EQUATION OF PERPENDICULAR BI SECTOR
– Let two point be A and B.
Where,
Line L is perpendicular bisector between point A and B.
Now our intention is to find the equation of L.
IMPORTANT STEPS
1. Determine the midpoint between point A and B.
2. Since L and 
are ⊥ to each other then find slope of L.
for
3. Get equation of L as equation of perpendicular bisector of 
by using 
and mid point of A and B.
THE COORDINATE OF THE FOOT OF PERPENDICULAR FROM THE POINT
THE POINT TO THE LINE
– -Our intention is to find the coordinate of the foot (x,y) which act as the point if intersection of 
and 
.
– Let consider the figure below.
