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

Answer:

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

Step-by-step 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 $J$.