#(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)#
