Question

Similar triangles RPQ and PMN are shown on the coordinate plane. Line ļ passes througe points M, P, and R.

select the list to correctly complete the Sentence the slope of segment RP is_______ the slope of segment PM
equal to
greater than
less than ​

Answer 1

is equal to

Explanation:

calculate the slopes m using the slope formula

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

let (x₁, y₁ ) = R (6, - 7 ) and (x₂, y₂ ) = P (- 2, 5 )

substitute these values into the formula for m

`m_(PR)` =
`(5-(-7))/(-2-6)` =
`(5+7)/(-8)` =
`(12)/(-8)` = -
`(3)/(2)`

let (x₁, y₁ ) = P (- 2, 5 ) and (x₂, y₂ ) = M (- 4, 8 )

substitute these values into the formula for m

`m_(PM)` =
`(8-5)/(-4-(-2))` =
`(3)/(-4+2)` =
`(3)/(-2)` = -
`(3)/(2)`

Thus

the slope of segment RP is equal to the slope of segment PM