Question

Draw the perpendicular bisector of $\overline{XY}$ whose length is $10.3cm$

If $M$ is the mid-point of $\overline{XY}$, what can you say about the lengths $MX$ and $XY$?

Answer 1

A perpendicular bisector of a line segment is a line segment perpendicular to and passing through the midpoint of the line segment.

Steps of construction:
(i) Draw a line segment $\overline{XY}=10.3cm$

(ii) Taking $X$ and $Y$ as centers and radius more than half of $XY,$ draw two arcs that intersect each other at $C$ and $D.$

(iii) Join $CD.$ Then $CD$ is the required perpendicular bisector of $\overline{XY}$

If M is the mid- point of $\overline{XY}$ then $\overline{MX}=\frac{1}{2}\overline{XY}=\frac{1}{2}\times 10.3=5.15cm$

$\overline{MX}=5.15cm$