Question

a line has a slope of negative - 4/5. which ordered pairs could be points on a line that is perpendicular to this line? select two options. a. (-2,0) and (2,5) b. (-4,5) and (4,-5) c. (-3,4) and (2,0) d. (1,-1) and (6,-5) e. (2,-1) and (10,9)

Answer 1

a and e

Explanation:

given a line with slope m = -
`(4)/(5)`

given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(4)/(5) )` =
`(5)/(4)`

use the slope formula to find which pair of points gives m =
`(5)/(4)`

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

(a) let (x₁, y₁ ) = (- 2, 0 ) and (x₂, y₂ ) = (2, 5 )

m =
`(5-0)/(2-(-2))` =
`(5)/(2+2)` =
`(5)/(4)` ← required slope

(b) let (x₁, y₁ ) = (- 4, 5 ) and (x₂, y₂ ) = (4, - 5 )

m =
`(-5-5)/(4-(-4))` =
`(-10)/(4+4)` =
`(-10)/(8)` = -
`(5)/(4)` ← incorrect slope

(c) let (x₁, y₁ ) = ( - 3, 4 ) and (x₂, y₂ ) = (2, 0 )

m =
`(0-4)/(2-(-3))` =
`(-4)/(2+3)` = -
`(4)/(5)` ← incorrect slope

(d) let (x₁, y₁ ) = (1, - 1 ) and (x₂, y₂ ) = (6, - 5 )

m =
`(-5-(-1))/(6-1)` =
`(-5+1)/(5)` = -
`(4)/(5)` ← incorrect slope

(e) let (x₁, y₁ ) = (2, - 1 ) and (x₂, y₂ ) = (10, 9 )

m =
`(9-(-1))/(10-2)` =
`(9+1)/(8)` =
`(10)/(8)` =
`(5)/(4)` ← required slope

the ordered pairs that could be points on the line are (a) and (e)