Important Straight Lines Formulas for JEE and NEET

 Page 1


Page # 2
STRAIGHT LINE
1 . Distance Formula:
2 2
1 2 1 2
d (x – x ) (y – y) ? ? .
2 . Section Formula :
x = 
n m
x x m
1 2
?
 ; y = 
n m
y y m
1 2
?
.
3 . Centroid, Incentre & Excentre:
Centroid G 
?
?
?
?
?
? ? ? ? ?
3
y y y
,
3
x x x
3 2 1 3 2 1
,
Incentre I ?
?
?
?
?
?
? ?
? ?
? ?
? ?
c b a
cy by ay
,
c b a
cx bx ax
3 2 1 3 2 1
Excentre  I
1
?
?
?
?
?
?
? ? ?
? ? ?
? ? ?
? ? ?
c b a
cy by ay
,
c b a
cx bx ax
3 2 1 3 2 1
4 . Area of a Triangle:
5 . Slope Formula:
Line Joining two points (x
1
 y
1
) & (x
2
 y
2
), m =
2 1
x x
y y
?
6 . Condition of collinearity of three points:
1 y x
x
y
3 3
2 2
1 1
 = 0
7 . Angle between two straight lines :
tan
 
? = 
2 1
2 1
m m
m m
?
?
.
MATHEMA TICS
FORMULA BOOKLET
Page 2


Page # 2
STRAIGHT LINE
1 . Distance Formula:
2 2
1 2 1 2
d (x – x ) (y – y) ? ? .
2 . Section Formula :
x = 
n m
x x m
1 2
?
 ; y = 
n m
y y m
1 2
?
.
3 . Centroid, Incentre & Excentre:
Centroid G 
?
?
?
?
?
? ? ? ? ?
3
y y y
,
3
x x x
3 2 1 3 2 1
,
Incentre I ?
?
?
?
?
?
? ?
? ?
? ?
? ?
c b a
cy by ay
,
c b a
cx bx ax
3 2 1 3 2 1
Excentre  I
1
?
?
?
?
?
?
? ? ?
? ? ?
? ? ?
? ? ?
c b a
cy by ay
,
c b a
cx bx ax
3 2 1 3 2 1
4 . Area of a Triangle:
5 . Slope Formula:
Line Joining two points (x
1
 y
1
) & (x
2
 y
2
), m =
2 1
x x
y y
?
6 . Condition of collinearity of three points:
1 y x
x
y
3 3
2 2
1 1
 = 0
7 . Angle between two straight lines :
tan
 
? = 
2 1
2 1
m m
m m
?
?
.
MATHEMA TICS
FORMULA BOOKLET
Page # 3
8.
ax + by + c = 0 and a ?x + b ?y + c ? = 0 two lines
1. parallel if
a
a
?
 =
b
b
?
 ? 
c
c
?
.
2. Distance between two parallel  lines  =
2 2
2 1
b a
c c
?
?
.
3 Perpendicular : If aa ? + bb ? = 0.
9. A point and line:
1. Distance between point and line =
a x by c
a b
1 1
2 2
? ?
?
.
2. Reflection of a point about a line:
2 2
1 1 1 1
b a
c by ax
2
b
y y
a
x x
?
? ?
? ?
?
?
?
3. Foot of the perpendicular from a point on the line is
2 2
1 1 1 1
b a
c by ax
b
y y
a
x x
?
? ?
? ?
?
?
?
10. Bisectors of the angles between two lines:
2 2
b a
c yb xa
?
? ?
 = ± 
2 2
b a
c yb xa
? ? ?
? ? ? ? ?
11. Condition of Concurrency :
of three straight lines a
i
x+ b
i
y + c
i
 = 0, i = 1,2,3 is
a b c
a b c
a b c
1 1 1
2 2 2
3 3 3
 = 0.
12. A Pair of straight lines through origin:
ax²
 
+ 2hxy
 
+ by² = 0
If ? is the acute angle between the pair of straight lines, then tan ?
= 
b a
b a h 2
2
?
?
.