Question

Point A(-4,1) is in standard (x,y) coordinate plane. What must be the coordinates of point B so that the line x=2 is the perpendicular bisector of ab?

Answer 1

Let,the coordinate of `B` is `(a,b)`

So,if `AB` is perpendicular to `x=2` then,its equation will be `Y=b` where `b` is a constant as slope for the line `x=2` is `90^@`, hence the perpendicular line will have a slope of `0^@`

Now,midpoint of `AB` will be `((-4+a)/2), ((1+b)/2)`

clearly,this point will lie on `x=2`

So, `(-4+a)/2=2`

or, `a=8`

And this will lie as well on `y=b`

so, `(1+b)/2 =b`

or, `b=1`

So,the coordinate is `(8,1)`