A(4,2), B(2,8)
AC: y=x-2
Point point form for a line through (a,b) and (c,d) is (c-a)(y-b)=(d-b)(x-a)
AB is (2 - 4)(y - 2) = (8-2)(x-4)
-2(y - 2)=6(x-4)
y - 2 = -3(x-4)
y = -3x + 14
BC is perpendicular through B, so slope 1/3 and we calculate the constant as y-(1/3)x:
y = (1/3) x + (8 - (1/3)(2) ) = (1/3) x + 22/3
a)Answer: BC is y = (1/3) x + 22/3
C is the meet of AC and BC,
x - 2 = (1/3) x + 22/3
3x - 6 = x + 22
2x = 28
x = 14
y = x-2 = 12
Check: y = (1/3)x + 22/3 = (14+22)/3 = 36/3 = 12 good
C(14,12)
The remaining corner is D. We have A-B=D-C or
D = A+C-B+C = (4,2)+(14,12)-(2,8) = (16, 6)
b)Answer: B(2,8) [given, but asked for] C(14,12), D(16,6)