Respuesta :

Answer:

perpendicular slope = [tex]\frac{7}{3}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (6, - 6) and (x₂, y₂ ) = (- 1, - 3)

m = [tex]\frac{-3+6}{-1-6}[/tex] = [tex]\frac{3}{-7}[/tex] = - [tex]\frac{3}{7}[/tex]

Given slope m then the slope of a perpendicular line is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{3}{7} }[/tex] = [tex]\frac{7}{3}[/tex]

as you saw on the previous posting, the slope of those points is -3/7, and any line perpendicular to it will have a negative reciprocal slope to that one.

[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{3}{7}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{7}{3}}\qquad \stackrel{negative~reciprocal}{\cfrac{7}{3}}}[/tex]

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