Consider the condition, Slope of BC‌times slope of AD=−1 Then the diagram is,
Now ‌
3+1
−2−5
×‌
k
h
=−1 ‌
k
h
×‌
4
−7
=−1 ‌
4k
−7h
=−1 4k−7h=0‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(I) And, Slope of AB× slope of CF=−1 so, MAB×MCF=−1 MAB×‌
−3
2
=−1 MAB=‌
2
3
So, the equation of AB is, y+1‌‌=‌
2
3
(x−5) 3y+3‌‌=2x−10 2x−3y‌‌=13 Here A(h,k) lies on AB so, 2h−3k=13‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(II) From equation (I) and (II), h=−4,k=−7 Hence third vertex of triangle is (-4,-7)