(1) Finding B.
Slope of AE.
(6-4)/(-1-3)=-1/2
Since AE is perpendicular to EB, the slope of BE is 2 (negative reciprocal of -1/2).
The (x, y) in here will be B's coordinates.
"Slope of BE"(2)=(y-4)/(x-3)
2x-6=y-4
2x-y=2
"Slope of AB"(1/3)=(y-6)/(x+1)
x+1=3y-18
x-3y=-19
Solve the system of equations:
2x-y=2
-2x+6y=38
5y=40
y=8,x=5
Thus B(5,8).
(2)
The height of Triangle EBC is the difference of y coordinates of B and E.
Which is 8-4=4
The base of the Triangle is the difference of the x coordinates of E and C
(The x coordinate of C is unkown.)
Which is (x-3).
Use the area of triangle area of EBC.
EBC=1/2(x-3)(4)
24=2x-6
x=15
Thus C(15,4)
(3) Finding D.
The slope of AE is the same as AD.
Thus:
AE=(y-4)/(x-3)
-1/2=(y-4)/(x-3)
But the x coordinate of C is the same as D.
-1/2=(y-4)/(15-12)
-3=2y-8
y=5/2
Thus: D(15,5/2)