Respuesta :
Answer:
[tex]k= \frac{-34}{3}[/tex]
Step-by-step explanation:
Step 1 :-
Perpendicular condition :-
Step 1:-
Two non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.
[tex]m_{2} = \frac{-1}{m_{1} }[/tex]
[tex]m_{1} m_{2} = -1[/tex]
Step 2:-
The given points are (-8,k) and (-4,-8)
[tex]m_{1} = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
finding slope of the first line is [tex]m_{1}[/tex]
using formula [tex]m_{1} = \frac{-8-k}{-4+8}[/tex]
= [tex]\frac{-8-k}{4}[/tex]
finding slope of the second line is [tex]m_{2}[/tex]
using formula [tex]m_{2} = \frac{--5+11}{5-10}[/tex]
= [tex]\frac{6}{-5}[/tex]
Step 3:-
using perpendicular condition
The two lines are perpendicular and their slopes are
[tex]m_{1} m_{2} = -1[/tex]
[tex](\frac{-k-8}{4} )(\frac{-6}{5} )= -1[/tex]
simplification,we get solution is
[tex]\frac{6(k+8)}{20} =-1[/tex]
[tex]6 k+48 =-20[/tex]
[tex]6 k = -20 -48[/tex]
[tex]6 k = -68[/tex]
[tex]\frac{-68}{6}[/tex]
[tex]k= \frac{-34}{3}[/tex]
Final answer is
[tex]k= \frac{-34}{3}[/tex]
