Matematică >> Drepta în plan >> 6
\( d \) : \( \displaystyle \frac {x - \color{red}x_A}{\color{orange}x_B \color{grey} - \color{red}x_A} = \frac {y - \color{blue}y_A}{\color{green}y_B \color{grey} - \color{blue}y_A} \).
\( d \) : \( \displaystyle \frac {x - \color{red}x_A}{\color{orange}x_B \color{grey} - \color{red}x_A} = \frac {y - \color{blue}y_A}{\color{green}y_B \color{grey} - \color{blue}y_A} \)
\( d \) : \( \displaystyle \frac {x - \color{red}3}{\color{orange}-2 \color{grey} - \color{red}3} = \frac {y - \color{blue}(-5)}{\color{green}6 \color{grey} - \color{blue}(-5)} \)
\( d \) : \( \displaystyle \frac {x - 3}{-5} = \frac {y + 5}{11} \)
\( d \) : \( 11( x - 3 ) = - 5( y + 5 ) \)
\( d \) : \( 11x - 33 = - 5y - 25 \)
\( d \) : \( 11x + 5y - 33 + 25 = 0 \)
\( d \) : \(11x + 5y - 8 = 0 \).
Ecuația dreptei \( d \) care trece prin punctele \( A( \color{red}-8 \color{grey}, \color{blue}0) \)
și \( B( \color{orange}-4 \color{grey}, \color{green}-7) \) este dată de formula:
\( d \) : \( \displaystyle \frac {x - \color{red}x_A}{\color{orange}x_B \color{grey} - \color{red}x_A} = \frac {y - \color{blue}y_A}{\color{green}y_B \color{grey} - \color{blue}y_A} \)
\( d \) : \( \displaystyle \frac {x - \color{red}(-8)}{\color{orange}-4 \color{grey} - \color{red}(-8)} = \frac {y - \color{blue}0}{\color{green}-7 \color{grey} - \color{blue}0} \)
\( d \) : \( \displaystyle \frac {x + 8}{4} = \frac {y }{-7} \)
\( d \) : \( -7( x + 8 ) = 4 y \)
\( d \) : \( - 7x - 56 = 4y \)
\( d \) : \( - 7x - 4y - 56 = 0 \).