Question

A point K is on the perpendicular bisector of a segment with endpoints at H and J. What must be true about point K? It is equidistant from H and J It falls on the h j It is at the midpoint of h j Not enough information is given

Answer 1

`K` is equidistant from
`H` and
`J`.

Explanation:

Given that the point
`K` which is on the perpendicular bisector of the line segment having endpoints at
`H` and
`J`.

The given situation can be represented as the diagram as attached in the answer area.

Referring to the
`\triangle HOK, \triangle JOK`:

`\angle HOK = \angle JOK=90^\circ` (As it is the perpendicular bisector)

`OH = OJ` (As it is the perpendicular bisector)

Also, the side
`OK` is the common side.

Therefore by
`S-A-S` congruence,
`\triangle HKO\cong \triangle JKO`

As per the properties of congruent triangles:

Side
`HK` = Side
`JK`

`HK` and
`JK` are nothing but the distance of the point
`K` from the end points
`H` and
`J` which are proved to be equal to each other.

Therefore, we can conclude that:

`K` is equidistant from
`H` and
`J`.