Answer:
x = 0
Step-by-step explanation:
The critical information we need to know here is that:
"the product of the slopes of 2 lines that are perpendicular is -1"
So we need to find the slope of each and multiply them and equate it to -1 and solve for x. First, we need to find the slope.
Slope is given by the formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where
x_1 and x_2 are the x coordinates of the points respectively, and
y_1 and y_2 are the y coordinates of the points respectively.
First, the slope of (3,4) and (8,-6) using formula above:
[tex]\frac{-6-4}{8-3}=\frac{-10}{5}=-2[/tex]
Secondly, the expression for slope of (2,4) and (x,3) using same formula:
[tex]\frac{3-4}{x-2}=\frac{-1}{x-2}[/tex]
Now we multiply both and equate to -1 and solve for x:
[tex]\frac{-1}{x-2}*(-2)=-1\\\frac{2}{x-2}=-1\\2=-1(x-2)\\2=-x+2\\x=2-2\\x=0[/tex]
Thus, the value of x is 0
