Question

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)

Answer 1

Options A and Option E.

Explanation:

A line has a slope of -4/5. Now a line perpendicular to this line will have the slope as
`m_(1).m_(2)=-1`

Therefore
`m_(2)=-(1)/(m_(1))=(1)/((4)/(5) )=(5)/(4)`

Now we will find the slope with the help of points given in the options if they lie on the perpendicular line.

A).
`m=(5-0)/(2+2)=(5)/(4)`

B).
`m=(-5-5)/(4+4)=(-10)/(8)=-(5)/(4)`

C).
`m=(0-4)/(2+3)=-(4)/(5)`

D).
`m=(-5+1)/(6-1)=(-4)/(5)=-(4)/(5)`

E).
`m=(9+1)/(10-2)=(10)/(8)=(5)/(4)`

Options A and E are the correct options.