CLASS XI STRAIGHT LINE DPP 1
STRAIGHT LINE
1. distance b/w two Points
A ____________________ B
(x₁,y₁) (x₂,y₂)
AB=√(x₂-x₁)²+(y₂-y₁)²
2. If A, B, C are collinear i.e A, B, C lies on a line then AB+BC=AC or
area of Δ = 0
x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)=0
3. Slope of straight line (S.L.) is the tangent of angle made by the line in
Anticlockwise direction of x-axis
4. Slope of x-axis = 0 {θ=0°}
5. slope of y-axis = ∞ {θ=90°}
6. A _______________________B
(x₁,y₁) (x₂,y₂)
Slope of AB= y₂-y₁ / x₂-x₁
7. Angle b/w two lines having slope m₁ and m₂ is
tanθ= | m₂-m₁ / 1+m₁m₂ |
8. For Parallel lines m₁=m₂.
9. For Perpendicular lines m₁.m₂=-1
10. Equation of S.L. which is Passing through (x₁,y₁) and Slope m
y-y₁=m(x-x₁)
11. Equation of S.L. which is Passing through (x₁,y₁) and (x₂,y₂)
y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)
12. Equation of S.L which cuts intercept a on x-axis, 'b' on y-axis
x/a + y/b =1 (intercept form)
13. Equation of S.L. on which length of ⊥ from origin is 'p' and this ⊥ makes
α with
x-anis
x cos α+ y sin α = p
(Normal form)
14. Equation of straight line which cut intercept 'c' on y-anis and having
slope m
y = mx + c
15. Equation of line Parallel to x-anis
y = a
16. Equation of line Parallel to y-anis
x = a
17. Standard form of S.L.
ax + by + c = 0
Ex. 3x + 5y + 9 = 0
etc.
18. Distance of a line ax+by+c from a Point, (x₁, y₁)
d = |ax₁ + by₁ + c|/√a² + b²
ax+by+c = 0
19. If we have given 'd' and find a variable x or y then we should put d as
±d.
20. distance b/w two Parallel lines:
let ax+by+c₁ = 0 --①
ax+by+c₂ = 0 --②
d = |c₁ - c₂| / √a² + b²
Note: two lines are Parallel If coefficients of x & y are
same.
21. Equation of a line Parallel to the
ax+by+c = 0 is
ax + by + k = 0, find k
by given condition.
22. Eq. of line ⊥ to ax+by+c=0 is bx - ay + k = 0, find k by using given
condition.
22. Conversion of ax+by+c=0 into slope intercept form (y=mx+c)
let equation ax+by+c=0
.: y = -a/b x - c/b
Here m = -a/b intercept on y-axis = -c/b
23. Conversion of ax+by+c into intercept form (x/a + y/b = 1)
Let Eq. is ax+by+c=0
ax+by=-c
divide by -c both sides -a/c x - b/c y = 1
Intercept on x-axis = -c/a
Intercept on y-axis = -c/b
24. Conversion of ax+by+c=0 into normal form (xcosα + ysinα = p)
we have ax+by+c=0
ax+by=-c
divide both side by √a²+b²
a/√a²+b² x + b/√a²+b² y = -c/√a²+b²
Here cos α = a / √(a² + b²), sin α = b / √(a² + b²)
Find common angle α which satisfy both cos and sin perp. from
origin = - c / √(a² + b²)
25. If two lines are Parallel then their slopes are equal m₁ = m₂.
26. If two lines are ⊥ then m₁ x m₂ = -1 or m₁ = -1/ m₂
27. To find equation of S.L. we should 1st think about Point of Passing of
line and slope of line by using given conditions.
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