If the points `A(1,3)`, `B(-2,1)`, `C(x,2)` and `D(-1,5)` are given and `AB` is perpendicular to `CD`, find the value of `x`.

Explanation

Slope of `AB=m_(1)=(1-3)/(-2-1)=(2)/(3)`
Slop of `CD=m_(2)=(5-2)/(-1-x)=(3)/(-1-x)`
Now, `AB` is perpendicular to `CD`.
`:. M_(1)*m_(2)=-1`
`(2)/(3)*((3)/(-1-x))=-1`
`implies 2=1+x`
`implies x=1`.