Question 620474
  <pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
1.The distance of the point (1,5) from the line y = -2 x - 1
Blue line perpendicular to y = -2x+1 that passes thru (1,5) would be y = (1/2)x + 9/2
When the lines Intersect: {{{ -2x+1 = (1/2)x + 9/2}}}     | x = (-11/5) and y = (17/5)
Distance between Points: D = {{{sqrt ((x[1]-x[2])^2+(y[1]-y[2])^2))}}}
(   1,    5)
(-11/5, 17/5)  D  = {{{sqrt( (16/5)^2 + (8/5)^2) = sqrt(320/25) =sqrt((64*5)/25)= (8/5)sqrt(5)}}}
{{{drawing(300,300,   -6, 6, -6, 6,   grid(1),
circle(1, 5,0.3),
circle(-11/5,17/5,0.3),
graph( 300, 300, -6, 6, -6, 6,0, -2x-1, .5x + 9/2))}}}

2. 2.The equation of the line that goes through the point ( 4 ,6 ) and is <u>perpendicular</u> to the line: 
4x + 2y = 3   or    y = -2x + 3/2,   m = -2
New Line:  m = (1//2)   the negative reciprocal of -2
 y = (1/2)x + b   |\using Pt(4,6) to solve for b
 6 = 2 + b
 4 = b    and y = (1/2)x +  4