Answer:
The slope of the line that is perpendicular to FG is [tex]\frac{12}{5}[/tex]
Step-by-step explanation:
step 1
Find the slope of line FG
we have
[tex]F(8,4),G(-4,9)[/tex]
[tex]m=\frac{9-4}{-4-8}[/tex]
[tex]m=\frac{5}{-12}[/tex]
[tex]m=-\frac{5}{12}[/tex]
step 2
Find the slope of the line that is perpendicular to FG
we know that
If two lines are perpendicular, then the product of their slopes is equal to -1 ( the slopes are inverse reciprocal each other)
so
[tex]m1*m2=-1[/tex]
we have
[tex]m1=-\frac{5}{12}[/tex]
substitute and solve for m2
[tex](-\frac{5}{12})*m2=-1[/tex]
[tex]m2=\frac{12}{5}[/tex]
therefore
The slope of the line that is perpendicular to FG is [tex]\frac{12}{5}[/tex]
