Question

Help please!
Slope of one of the dotted lines:


Slope of the line reflection:

Answer 1

Dotted line =1/3
Line reflection=-3

Answer 2

see explanation

Explanation:

calculate slope m using the slope formula

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

consider the slope of the middle dotted line

with (x₁, y₁ ) = (- 3, - 4) and (x₂, y₂ ) = (3, - 2) ← 2 points on the line

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

consider the slope of the line of reflection ( the solid line )

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (- 2, 3) ← 2 points on the line

m =
`(3-0)/(-2-(-1))` =
`(3)/(-2+1)` =
`(3)/(-1)` = - 3

note the product of the slopes =
`(1)/(3)` × - 3 = - 1

indicating the lines are perpendicular to each other