Elemente de geometrie analitica

Distanta dintre doua puncte A(x₁, y₁), B(x₂, y₂):

• $AB=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

• $AB=\sqrt{\left(x_1+x_2\right)}+\sqrt{\left(y_1+y_2\right)}$

Panta dreptei AB

• $m_{AB}=\frac{y_2-y_1}{x_2-x_1}$

• $m_{AB}=\frac{x_2-x_1}{y_2-y_1}$

Coordonatele (x,y) ale mijlocului segmentului AB

• $x=\frac{x_1+x_2}{2},\ y=\frac{y_1+y_2}{2}$

• $x=\frac{x_2-x_1}{2},\ y=\frac{y_2-y_1}{2}$

Ecuatia dreptei de panta m, prin punctul (x₀, y₀)

• $y-y_0=n\left(x-x_0\right)$

• $y-y_0=m\left(x-x_0\right)$

Doua drepte sunt oerpendiculare daca :

• $m_1m_2=1$

• $m_1m_2=-1$