Question

determine the value of x that the line containing (3,4) and (8,-6) is perpendicular to the line containing (2,4) and (x,3)

Answer 1

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:

$\frac{y_2-y_1}{x_2-x_1}$

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:

$\frac{-6-4}{8-3}=\frac{-10}{5}=-2$

Secondly, the expression for slope of (2,4) and (x,3) using same formula:

$\frac{3-4}{x-2}=\frac{-1}{x-2}$

Now we multiply both and equate to -1 and solve for x:

$\frac{-1}{x-2}*(-2)=-1\\\frac{2}{x-2}=-1\\2=-1(x-2)\\2=-x+2\\x=2-2\\x=0$

Thus, the value of x is 0