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A line has a slope of -4/5 . Which ordered pairs could be points on a line that is perpendicular to this line? Check all that apply.


(–2, 0) and (2, 5)

(–4, 5) and (4, –5)

(–3, 4) and (2, 0)

(1, –1) and (6, –5)

(2, –1) and (10, 9)

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Answer:

Step-by-step explanation:

Given that a  line has a slope of \(\frac{-4}{5}\)

For any line perpendicular to this line,

the slope of the line = \(\frac{-1}{slope of the given line} \\=\frac{-1}{\frac{-4}{5} } \\=\frac{5}{4}\)

Let us check whether the given options satisfy this

a) (-2,0) and (2,5)... slope = \(\frac{5-0}{2-(-2)} =\frac{5}{4}\)

Yes true

b) (–4, 5) and (4, –5)... slope = \(\frac{-5-5}{4-(-4)} =\frac{-5}{4}\)

No not true.

c) (–3, 4) and (2, 0)

Slope = \(\frac{-4}{5}\)

No not true.

d) (1, –1) and (6, –5)

Slope = \(\frac{-5+1}{6-1} =\frac{-4}{5}\)

No, not true.

e) (2, –1) and (10, 9)

Slope = 5/4

True.

e) (2, –1) and (10, 9)