AP EAMCET Engineering 21 Apr 2019 Shift 2 Paper

Consider the equation of perpendicular bisector is y=mx+c
The intercept is 1, thus the equation becomes y=mx+1
The mid-point of the points A(α,3) and B(2,−1) is (‌

α+2

2

,1)
since the equation passes through (‌

α+2

2

,1)
Thus,
1=m(‌

α+2

2

)+1
2=m(α+2)+2
m(α+2)=0
mα+2m=0‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(I)
Here, m is the gradient of the perpendicular line.
m=−(‌

α−2

4

)
Substitute the value in equation (I).
α(‌

2−α

4

)+2(‌

2−α

4

)=0
α=±2