The lines shown below are perpendicular. If the green line has a slope of a

Mathematics

1 answer:

Georgia [21]3 years ago

6 0

Answer:

-4/3

Step-by-step explanation:

since the both lines are perpendicular the product of their slopes equals -1
let m be the slope of the red line
m*a = -1
m = -1/a
a = (8-5)/(0-(-4)) = 3/4
so m = -4/3

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Use an equation to find the value of k

Delvig [45]

$\boxed{k=4}$

<h2>Explanation:</h2>

We know that the slope of a line is given by:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ Where: \\ \\ (x_{1},y_{1}) \ and \ (x_{2},y_{2}) \ are \ points \ that \ lie \ on \ the \ line \\ \\ \\ Here: \\ \\ (x_{1},y_{1})=(-2,k) \\ \\ (x_{2},y_{2})=(2,0) \\ \\ m=-1 \\ \\ \\ -1=\frac{0-k}{2-(-2)} \\ \\ -1=\frac{-k}{4} \\ \\ -k=4(-1) \\ \\ \boxed{k=4}$