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 \( A( \color{red}4 \color{grey}, \color{blue}6) \)
și \( B( \color{orange}-7 \color{grey}, \color{green}9) \) este dată de formula:
\( d \) : \( \displaystyle \frac {x - \color{red}x_A}{\color{orange}x_B \color{grey} - \color{red}x_A} = \frac {y - \color{blue}y_A}{\color{green}y_B \color{grey} - \color{blue}y_A} \)
\( d \) : \( \displaystyle \frac {x - \color{red}4}{\color{orange}-7 \color{grey} - \color{red}4} = \frac {y - \color{blue}6}{\color{green}9 \color{grey} - \color{blue}6} \)
\( d \) : \( \displaystyle \frac {x - 4}{-11} = \frac {y - 6}{3} \)
\( d \) : \( 3( x - 4 ) = -11( y - 6 ) \)
\( d \) : \( 3x - 12 = - 11y + 66 \)
\( d \) : \( 3x + 11y - 12 - 66 = 0 \)
\( d \) : \( 3x + 11y - 78 = 0 \).