CHAPTER
9 Straight Lines
Sr.
Concept Formulas Other information
No.
1. Distance Formula
PQ = ( x2 − x1 )2 + ( y2 − y1 )2 Distance between the points
P ( x1, y1 ) and Q ( x2 , y2 )
2. Section Formula mx + nx1 my2 + ny1 The coordinates of a point
(i) Internal division: 2
m + n
,
m+n dividing the line segment
joining the points ( x1, y1 )
(ii) External division:
and ( x2 − y2 ) in the ratio
mx2 − nx1 my2 − ny1
m−n , m−n m: n .
Mid point formula
x2 + x1 y2 + y1
2 , 2
3. Area or Triangle Area of a triangle, whose vertices are
( x1, y1 )( x2 , y2 ) and ( x3 , y3 ) is
1
= x1 ( y2 − y3 ) + x2 ( y3 − y1 ) + x3 ( y1 − y2 )
2
4. Slope m = tan, 90 The slope of a line is
denoted by m.
The slope (m) of a non-vertical line passing
through the points ( x1, y1 ) and ( x2 , y2 ) is
given by
y2 − y1
m= ,x x
x2 − x1
5. Angle between 2 lines An acute angle, , between l1 and l2 is given
m2 − m1
by tan = ,1 + m1m2 0
1 + m1m2
l1 is parallel to l2 if and only if m1 = m2 ,
JEE (XI) MATHEMATICS 1
9 Straight Lines
Sr.
Concept Formulas Other information
No.
1. Distance Formula
PQ = ( x2 − x1 )2 + ( y2 − y1 )2 Distance between the points
P ( x1, y1 ) and Q ( x2 , y2 )
2. Section Formula mx + nx1 my2 + ny1 The coordinates of a point
(i) Internal division: 2
m + n
,
m+n dividing the line segment
joining the points ( x1, y1 )
(ii) External division:
and ( x2 − y2 ) in the ratio
mx2 − nx1 my2 − ny1
m−n , m−n m: n .
Mid point formula
x2 + x1 y2 + y1
2 , 2
3. Area or Triangle Area of a triangle, whose vertices are
( x1, y1 )( x2 , y2 ) and ( x3 , y3 ) is
1
= x1 ( y2 − y3 ) + x2 ( y3 − y1 ) + x3 ( y1 − y2 )
2
4. Slope m = tan, 90 The slope of a line is
denoted by m.
The slope (m) of a non-vertical line passing
through the points ( x1, y1 ) and ( x2 , y2 ) is
given by
y2 − y1
m= ,x x
x2 − x1
5. Angle between 2 lines An acute angle, , between l1 and l2 is given
m2 − m1
by tan = ,1 + m1m2 0
1 + m1m2
l1 is parallel to l2 if and only if m1 = m2 ,
JEE (XI) MATHEMATICS 1
