Question

The perpendicular bisector of a line segment AB passes through the origin. If the
coordinates of A are (4,0), then find the coordinates of B and the length of AB​

Answer 1

Answer:

The given points are A(x

1

,y

1

)=(1,5) and B(x

2

,y

2

)=(4,6).

The perpendicular bisector of AB will pass through the midpoint of AB.

Now the perpendicular bisector of AB will meet Y axis at P(0,y).

∴AP=BP

Applying distance formula, we get

⇒AP

2

=BP

2

⇒(x

1

−0)

2

+(y

1

−y)

2

=(x

2

−0)

2

+(x

2

−y)

2

⇒(1−0)

2

+(5−y)

2

=(4−0)

2

+(6−y)

2

After solving, we get y=13

Therefore, the point is (0,13).