Question 390297
  <pre><font size = 3 color = "indigo"><b>
Hi
Midpoint ( {{{(x[1] + x[2])/2}}}, {{{(y[1] + y[2])/2}}})
Midpoint for line segment joining(-2,12) and (4,-6). 
 Midpoint is Pt(1, 3) slope of that segment is -6-12  / 4-(-2) = -18/6 = -3
slope of segment joining (4,4) and (1,3) is 3-4  /1-4 = -1/-3 = 1/3
slopes of two segments are negative reciprocals of one another, 
thus segments &#8869; to one another.
{{{drawing(300,300, -15,15,-15,15,
 grid(1),
circle(-2, 12,0.6),
circle(4, -6,0.6),
line(-2,12,4,-6),
circle(4, 4,0.6),
circle(1, 3,0.6),
line(4,4,1,3),
graph( 300, 300, -15,15,-15,15))}}}

2) find the value of K for which the line joining (2.1,3.3) and (K,-3.2) is parallel to the line joining (-1,-2) and (1,3). 
parallel lines have identical slopes
line joining (-1,-2) and (1,3) has slope:   3-(-2) / 1-(-1) = 5/2
line joining (2.1,3.3) and (K,-3.2): -3.2 - 3.3 / K - 2.1 =  -6.5/(K - 2.1)
-6.5/(K - 2.1) = 5/2  
5(K-2.1) = -2*6.5
5K - 10.5 = -13
 5K = -2.5
  K = -.5