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# Draw the perpendicular bisector of $ \overline{X Y} $ whose length is $ 10.3 \mathrm{~cm} $.

**(a)** Take any point $ \mathrm{P} $ on the bisector drawn. Examine whether $ \mathrm{PX}=\mathrm{PY} $.

**(b)** If $ \mathrm{M} $ is the mid point of $ \overline{\mathrm{XY}} $, what can you say about the lengths $ \mathrm{MX} $ and $ \mathrm{XY} $ ?

**To do:**

We have to draw the perpendicular bisector of $\overline{XY}$ whose length is $ 10.3\ cm$ and answer the given questions.

**Solution:**

**
**

__Steps of construction:__**
**

(i) Let us draw a line segment $\overline{XY}$ of length $ 10.3\ cm$ .

(ii) Now, with compasses take a measure greater than half of the length $\overline{XY}$

(iii) Now, by pointing the pointer of the compasses at point X and point Y respectively. let's draw two arcs above the line segment $\overline{XY}$ cutting each other and point it as C.

(iv) Similarly, by pointing the pointer of the compasses at point X and point Y respectively. let's draw another two arcs below the line segment $\overline{XY}$ cutting each other and point it as D.

(iv) Then, let's draw a line segment joining point C and point D.

(v) Therefore, the perpendicular bisector of the line segment $\overline{XY}$ is formed.

(a) Let us take any point P on the bisector CD.

Since $\overline{CD}$ is the perpendicular bisector of $\overline{XY}$ any point lying on $\overline{CD}$ will be at the same distance from point X and point Y of line segment $\overline{XY}$.

Therefore,

We may measure the length of $PX = PY$.

(b) As M is the midpoint of $\overline{XY}$. The perpendicular bisector $\overline{CD}$ passes through point M.

Therefore,

The length of $\overline{XY}$ is twice $\overline{MX}$.

That is $\overline{MX}$ is $\frac{1}{2}\overline{XY}$.

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