AP EAMCET Engineering 21 Apr 2019 Shift 1 Paper

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)