Answer:
Answer is given below with explanations.
Step-by-step explanation:
[tex]the \: equation \: of \: the \: line \: passing \: \\ through \: ( - 9, - 14) \: and \: (3,2) \: is \\ \frac{y - y1}{y2 - y1} = \frac{x - x1}{x2 - x1} \\ here \: x1 = - 9 \: \: \: y1 = - 14 \: \: \: \\ x2 = 3 \: \: \: \: y2 = 2 \\ \frac{y - ( - 14)}{2 - ( - 14)} = \frac{x - ( - 9)}{3 - ( - 9)} \\ \frac{y + 14}{2 + 14} = \frac{x + 9}{3 + 9} \\ \frac{y + 14}{16} = \frac{x + 9}{12} \\ \frac{y + 14}{4} = \frac{x + 9}{3} \\ 3(y + 14) = 4(x + 9) \\ 3y + 42 = 4x + 36 \\ 4x - 3y - 6 = 0 \\ the \: equation \: of \: the \: line \: perpendicular \: to \: \\ 4x - 3y - 6 = 0 \: is \: 3x + 4y + k = 0 \\ since \: it \: passes \: through \: ( - 3, - 6) \\ that \: is \: the \: midpoint \: of \: line \: segment \\ 3( - 3) + 4( - 6) + k = 0 \\ - 9 - 24 + k = 0 \\ k = 33 \\ the \: require \: equation \: is \: 3x + 4y + 33 = 0[/tex]
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