Analytic Geometry - Straight Line in Plane 1

Selasa, 19 Mei 2020

Straight Line in Plane

 

• Point Direction Form

     

Where (X, Y) is the direction of the line and P₁ (x₁, y₁) lies on the line.

 

figure

 

• Vertical Line

x = a

 

• Horizontal Line

y = b

 

• Vector Equation of a Straight Line

Where

O is the origin of the coordinates,

X is the position vector of direction, parallel to the line, t is a parameter,

 is the position vector of any poin X on the line.

 

Figure

 

• Straigt Line in Parametric Form

where

(x, y) are the coordinates of any unknown point on the line,

(x, y) are the coordinates of a known point on the line,

(x, y) are the coordinates of a vector parallel to the line,

T is a parameter.

 

Figure

 

• distance Form a Point To a Line

the distance from the point P(A, B) to the line Ax + By + C = 0 is

 

Figure

 

• Parallel Line

The lines y = k₁x + b₁ and y = k₂x + b₂ are parallel if k₁ = k₂.

The lines A₁x + B₁y + C₁ = 0 and A₂x + B₂y + C₂ = 0 are parallel if

 

Figure

 

 

• ·Perpendicular Line

The lines y = k₁x + b₁ and y = k₂x + b₂ are perpendicular ifor , equivalently, k₁ k₂ = – 1.

The lines A₁x + B₁y + C₁ = 0 and A₂x + B₂y + C₂ = 0 are perpendicular if A₁ A₂ + B₁ B₂ = 0.

 

 

Figure

 

 

• Angle Between Two Line

 

Figure

 

• Intersection of Two Line

If two lines A₁x + B₁y + C₁ = 0 and A₂x + B₂y + C₂ = 0 intersection, the intersection point has coordinanates.

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