Answer:
[tex]\frac{12}{5}[/tex]
Step-by-step explanation:
First, we need to find the gradient (slope) of the FG line.
To do this we must use the gradient formula:
[tex]\frac{y2 - y1}{x2 - x1}[/tex]
y1 and x1 have to be in the same coordinate set,
x1 = 8, y1 = 4 the (8 , 4) set
x2 = -4, y2 = 9 the (-4 , 9) set
[tex]\frac{9 - 4}{-4 - 8}[/tex]
[tex]\frac{5}{-12}[/tex]
Which is the gradient of FG line.
To find the equation of a line perpendicular to this line, you must do [tex]\frac{-1}{gradient}[/tex]
[tex]\frac{-1}{\frac{5}{-12} }[/tex]
= [tex]\frac{12}{5}[/tex]
So that means the gradient of the line perpendicular to FG is
[tex]\frac{12}{5}[/tex]
