Question

Given the points C(-1,5) and D(3,-1). Find the slope of a line parallel and

perpendicular to CD in simplest fractional form.

Answer 1

parallel slope = -
`(3)/(2)` , perpendicular slope =
`(2)/(3)`

Explanation:

calculate the slope m of CD using the slope formula

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

with (x₁, y₁ ) = C (- 1, 5 ) and (x₂, y₂ ) = D(3, - 1 )

m =
`(-1-5)/(3-(-1))` =
`(-6)/(3+1)` =
`(-6)/(4)` = -
`(3)/(2)`

• Parallel lines have equal slopes

the slope of a line parallel to CD is m = -
`(3)/(2)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(3)/(2) )` =
`(2)/(3)`

the slope of a line perpendicular to CD is m =
`(2)/(3)`