Analytic Geometry - Straight Line in Plane

Rabu, 20 Mei 2020

Straight Line in Plane

 

Poin coordinates: X, Y, X, x₀, x₁, y₀, y₁, a₁, a₂, ...

Real number: k, a, b, p, t, A, B, C, A₁, A₂, ...

Area: α, β

Area between two lines: φ

Normal vector:

Positive vector: 

• General Equation of a Straight Line

    Ax + By + C = 0

 

• Normal Vector to a Straight Line

   The vector  (A, B) is normal to the line Ax + By + C = 0.

 

Figure

 

• Explicit Equation of a Straight Line (Slope- Intercept Form)

    y = kx + b.

   The gradient of the line is k = tan α.

 

Figure

 

• Gradient of a Line

     

 

Figure

 

 

• Equation of a Line Given a Point and the Gradient

   y = y₀ + k(x – x₀),

   where k is the gradient, P(x₀, y₀) is a point on the line.

 

 

Figure

 

• Equation of a Line That Passes Through Two Points

    

Figure

 

 

• Intercept Form

     

 

Figure

 

• Normal Form

   x cos β + y sin β – p = 0

 

Figure

Sumber

Labels: Mathematician

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