Question

5. 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
pen​

Answer 1

Given:

The perpendicular bisector of a line segment AB passes through the origin. If the  coordinates of A are (4, 0)

To find:

The coordinates of B and the length of AB

Solution:

Let the coordinates of point B are (x, y)

As per the given condition, the origin would be the mid-point of the line segment AB.

And the coordinates of the origin are (0, 0)

and the formula of the coordinates of the mid-point is given by:

x = x1+x2/2, y = y1+y2/2

Putting the value of the coordinates:

0 = 4 + x/2, 0 = 0 + y/2

4 + x = 0, 0+ y = 0

x = -4 and y = 0

So the coordinates of the point B is (-4, 0)

and the length of the line segment AB is given by:

• $\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}$
• $\sqrt{(4+4)^{2}+(0+0)^{2}}$
• $\sqrt{(8)^{2}}$
• 8

Hence length of the line segment AB is 8 units