Answer:
The slope of the line that is perpendicular to DE is [tex]-\frac{6}{7}[/tex]
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Step 1
Find the slope DE
we have
[tex]D(7,4)\ E(1,-3)[/tex]
Substitute the values in the formula
[tex]m=\frac{-3-4}{1-7}[/tex]
[tex]m=\frac{-7}{-6}[/tex]
[tex]m=\frac{7}{6}[/tex]
Step 2
we know that
If two lines are perpendicular
then
the product of their slopes is equal to minus one
so
[tex]m1*m2=-1[/tex]
Find the slope of the line perpendicular to DE
we have
[tex]m1=\frac{7}{6}[/tex]
find m2
substitute and solve for m2
[tex]\frac{7}{6}*m2=-1[/tex]
[tex]m2=-\frac{6}{7}[/tex]
