Question 363854
<pre><font size = 3 color = "indigo"><b>
Hi, 
a. Show the triangle is right angled
mAB = -2/1  mBC = 2/4 = 1/2   
AB is perpendicular to BC as their slopes are negative reciprocals.
b.  Co-ordinates of the Point D such that ABCD is a rectangle
BC and AD would be parallel and have same slope = 1/2
y = 1/2x + b Using point (3,2) b = -1/2
y = .5x + .5 (red line) mCD = -2  CD meets AD at (7,4)

{{{drawing(500, 500, -1, 10, -1, 10,
line(3,2,4,0),
line(4,0,8,2),
line(8,2,3,2),
line(8,2,7,4),
locate(3.3,2.4,"A"),
locate(4.3,0.4,"B"),
locate(8.3,2.1,"C"),
locate(7.3,4.1,"D"),grid(1),
graph( 500, 500, -1, 10, -1,10,.5x+.5))}}}