Answer:
Option C [tex]-7x-5y=-48[/tex]
Step-by-step explanation:
step 1
Find the slope of AB
we have
A(-3,-1) and B(4,4)
The slope m is equal to
[tex]m=(4+1)/(4+3)[/tex]
[tex]m=5/7[/tex]
step 2
Find the slope of BC
we know that
If two lines are perpendicular, then the product of their slopes is equal to -1
so
[tex]m1*m2=-1[/tex]
we have
[tex]m1=5/7[/tex]
substitute
[tex]5/7*m2=-1[/tex]
[tex]m2=-7/5[/tex]
step 3
Find the equation of the line into slope point form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-7/5[/tex]
[tex]B(4,4)[/tex]
substitute
[tex]y-4=-(7/5)(x-4)[/tex]
Multiply by 5 both sides
[tex]5y-20=-7x+28[/tex]
[tex]7x+5y=28+20[/tex]
[tex]7x+5y=48[/tex]
Multiply by -1 both sides
[tex]-7x-5y=-48[/tex]
