(1) Finding B.
Slope of AE.
6−4−1−3=−12
Since AE is perpendicular to EB, the slope of BE is 2 (negative reciprocal of −12).
The (x,y) in here will be B's coordinates.
Slope of BE(2)=y−4x−3
2x−6=y−4
2x−y=2
Slope of AB(13)=y−6x+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=12(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−4x−3
−12=y−4x−3
But the x coordinate of C is the same as D.
−12=y−415−12
−3=2y−8
y=52
Thus: D(15,52)
