Line ℓ has equation y= - x–3. Find the distance between ℓ and the point B( - 4, - 2).

Question

This assignment is really hard... Please help?

Answer 1

The line with equation y = -x-3 has slope -1.

 

The line perpendicular to the given line and which passes through the point (-4,-2) has equation 

y - (-2) = (1)(x - (-4)).

 

y + 2 = x + 4

 

       y = x + 2

 

y = -x - 3 and y = x + 2 intersect when -x - 3 = x + 2

 

                                                               2x = -5

 

                                                                 x = -5/2   y = x + 2 = -1/2

 

Point of intersection = (-5/2, -1/2)

 

Distance between the given line and the point (-4,-2) 

 

   = distance between (-5/2, -1/2) and (-4, -2)

 

   = √ [ (-5/2-(-4))² + (-1/2-(-2))² ]

 

   = √ [ 9/4 + 9/4] = √(18/4) = 3√2/2