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?

oliadas73
2022-09-06
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Matthew Benton

Answered 2022-09-07
Author has **9** answers

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 $90}^{\circ$, hence the perpendicular line will have a slope of $0}^{\circ$

Now,midpoint of AB will be $\left(\frac{-4+a}{2}\right),\left(\frac{1+b}{2}\right)$

clearly,this point will lie on x=2

So, $\frac{-4+a}{2}=2$

or, a=8

And this will lie as well on y=b

so, $\frac{1+b}{2}=b$

or, b=1

So,the coordinate is (8,1)

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 $90}^{\circ$, hence the perpendicular line will have a slope of $0}^{\circ$

Now,midpoint of AB will be $\left(\frac{-4+a}{2}\right),\left(\frac{1+b}{2}\right)$

clearly,this point will lie on x=2

So, $\frac{-4+a}{2}=2$

or, a=8

And this will lie as well on y=b

so, $\frac{1+b}{2}=b$

or, b=1

So,the coordinate is (8,1)

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