This is a document based on straight lines specially for XI Std. This is based on its various forms of equations, Formula.

1. Kendriya Vidyalaya
Karwar
Math’s Project
2012-2013

2. Welcome to my
PowerPoint
presentation

3. Topic : Straight Line
By: Atit S Gaonkar

5. IndexA

6. EQUATIONS
A GLANCE AT X MATHS
A LINESLOPE OF
INDEXA

7. A Glance At ‘X’ Maths
• Distance Formula :
Let P(x1, y1) & Q (x2, y2)
PQ = ( [x2-x1]2 + [y2-y1]2 )

8. • Section formula :
If The Line Joining the Points P(x1, y1) & Q (x2, y2)
and in ratio m : n , the coordinates are
( [mx2+ nx1] / [m + n] , [my2+ ny1] / [m + n] )
• If m = n ; the coordinates of point are
([x2+ x1] / 2 , [y2+ y1] / 2 )

9. • The Area Of the Triangle whose vertices are
P(x1, y1) , Q (x2, y2) & R (x3, y3) equals
1/2 | x1(y2-y3) + x2(y3-y1) + x3(y1-y2) | .
• If the area equals zero then, the three points are
collinear.

10. • The Angle θ made by the line l with the positive
direction of x-axis and measured anti-clockwise, this
is called the slope or inclination.
• m = tan θ , where θ ≠ 90◦ .
Slope Of A Line

11. • Slope Of A Line When Any Two Points Of A Line
Are Given.
• ( [y2-y1] / [x2-x1] ).
• So, the slope of the line through the points P(x1, y1)
& Q (x2, y2) is given by
( [y2-y1] / [x2-x1] )

12. • Conditions For Parallelisms .
• Let we consider line l1 with it’s slope m1, and
another line l2 with it’s slope m2 .
• So, for the lines l1 & l2 to be parallel m1 should be
equal to m2 .
• i.e. m1 = m2

13. • Conditions For Perpendicularity .
• Let we consider line l1 with it’s slope m1, and
another line l2 with it’s slope m2 .
• So, for the lines l1 & l2 to be perpendicular the
products of the slopes should be equal to -1.
• i.e. m1 * m2 = -1

14. • Angle Between Two Lines.
• If we consider any line l1 passing through another
line l2 then there can be two angles :
• θ & (180 - θ ) = Φ
• tan θ = | [ m1 - m2 ] / [1 + m1m2 ] |

16. BLAH
BLAH
BLAH
BLAH
B
BLAH
BLAH
Equations of straight line

17. • If A Line Passes Through P(x1, y1) the equation of
the line is
m = ( [y-y1] / [x-x1] )
[y-y1] = m [x-x1]
1
Point
Slope Form

18. • Thus the point P(x1, y1) lies on the line with slope m
through the fixed points (x1, y1) if and only if, its
coordinates satisfy the equation
• [y-y1] = m [x-x1].

19. Two
Point Form• If a line passes from two points
P(x1, y1) & Q (x2, y2), then the equation of the line
passing through these points is
( [y-y1] / [x-x1] ) = [y2 -y1] / [x2-x1]
• ( [y-y1] ) = ( [y2 -y1] [x-x1] / [x2-x1] )
2

20. Slope
Intercept Form Suppose a line l with slope m, cuts the y-axis at a
distance ‘c’ from the origin, then ‘c’ is called the
y-intercept .
• So the equation of the line will be
[y-c] = m [x-0]
y = mx + c
3

21.  Suppose a line l with slope m, cuts the x-axis at a
distance ‘d’ from the origin, then ‘d’ is called the
x-intercept .
• So the equation of the line will be :
y = m (x – d)

22. Intercept form
• Suppose a line makes x-intercept
‘a’ and y-intercept ‘b’ on the axes, so qbviously
the line meets at (x, 0) & (0, y). So by two point
form the equation of the line is:
x / a + y / b = 1
4

23. Normal Form
• Suppose a non vertical line is known to us with the
following data :
Length of the perpendicular (normal) ‘p’ from the
origin to the line.
Angle θ which normal makes with the x-axis in
positive direction.
The slope of the line will be m = - ( cos θ ) / ( sin θ )
5

24. • So the equation of the line will be :
x cos ω + y sin ω = p.

25. BLAH
BLAH
BLAH
BLAH
B
BLAH
BLAH
General
Equations
of line

26. • The equation of first degree in two variables in the
form :
Ax + By + c = 0 , Where A, B & C are real
constants
1
The General
form

27. Slope
Intercept Form
• y = mx + c ; So in general equation form the
equation will be :
y = (-A / B ) x – ( C / B ) , where
m = (-A / B ) & c = – ( C / B )
2

28. Intercept Form
 x / a + y / b = 1, The equation in the general
form will be :
x / (-A / B) + y / (-C / B) = 1, where
x-intercept is (-A / B) & y-intercept is (-C / B)
3

29. Normal form
• x cos ω + y sin ω = p , the equation in the
general form will be :
A/( A2 + B2 )1/2 x + B/( A2 + B2 ) 1/2 y = C/( A2 + B2 )
where cos ω = ± A/( A2 + B2 )1/2
sin ω = ± B/( A2 + B2 ) 1/2
c = ± C/( A2 + B2 ) 1/2
4

30. • The distance of a line Ax + By + C = 0
perpendicular to the point P(x1, y1) is given by ‘d’.
d = | (Ax1 + By1 + C ) / (A2 + B2 ) 1/2 |
Distance Of A Point
From A Line

31. • Let two lines be :
y = mx + c1 .
y = mx + c2 .
Then the perpendicular distance between the two
line is given by ‘d’.
d = | c1 – c2 | / ( 1 + m2 ) 1/2
Distance Between
two parallel Line

32. • Let two lines be :
Ax + By + C1 = 0
Ax + By + C2 = 0
Then the perpendicular distance between the two
line is given by ‘d’.
d = | C1 – C2 | / ( A2 + B2 ) 1/2