Question

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.Prove: Every point on the perpendicular bisector of a segment is equidistant from the ends of the segment.AP = BP

Answer 1

The diagram is given with coordinates

`A(-a,0),P(0,b),B(a,0)`

To find the value of AP,

`AP=\sqrt[]{(0-(-a))^2+(b-0)^2}`
`AP=\sqrt[]{a^2+b^2}`

To find the value of BP.

`BP=\sqrt[]{(a-0)^2+(0-b)^2}`
`BP=\sqrt[]{a^2+b^2}`

Hence it is proved that AP=BP.