Answer:
[tex]x=-9[/tex]
Step-by-step explanation:
Perpendicular lines means that their slopes are negative reciprocals of each other.
In other words, when you multiply the 2 slopes, that will gives us -1.
Slope's formula is m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\frac{y_2-y_1}{x_2-x_1}\\=\frac{2--6}{7-11}\\=\frac{8}{-4}\\=-2[/tex]
[tex]\frac{-2-4}{x-3}\\=\frac{-6}{x-3}[/tex]
Now multiplying these 2 expressions and equating it to -1, we can solve for x:
[tex]-2*\frac{-6}{x-3}=-1\\\frac{12}{x-3}=-1\\12=-1(x-3)\\12=-x+3\\x=3-12\\x=-9[/tex]
x = -9
