Answer:
Step-by-step explanation:
Given that a line has a slope of [tex]\frac{-4}{5}[/tex]
For any line perpendicular to this line,
the slope of the line = [tex]\frac{-1}{slope of the given line} \\=\frac{-1}{\frac{-4}{5} } \\=\frac{5}{4}[/tex]
Let us check whether the given options satisfy this
a) (-2,0) and (2,5)... slope = [tex]\frac{5-0}{2-(-2)} =\frac{5}{4}[/tex]
Yes true
b) (–4, 5) and (4, –5)... slope = [tex]\frac{-5-5}{4-(-4)} =\frac{-5}{4}[/tex]
No not true.
c) (–3, 4) and (2, 0)
Slope = [tex]\frac{-4}{5}[/tex]
No not true.
d) (1, –1) and (6, –5)
Slope = [tex]\frac{-5+1}{6-1} =\frac{-4}{5}[/tex]
No, not true.
e) (2, –1) and (10, 9)
Slope = 5/4
True.
e) (2, –1) and (10, 9)
