Draw the perpendicular bisector of $\overline{XY}$ whose length is 8.3 cm.

(i) Take any point P on the bisector drawn. Examine whether PX = PY.

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

Steps:

1. Draw a line segment $\overline{XY}$ of length 8.3 cm.

2. With X as centre and any suitable radius $\left(\gt\dfrac{1}{2}\text{XY}\right)$, draw arcs on each side of $\overline{XY}$.

3. With Y as centre and the same radius, draw arcs on each side of $\overline{XY}$ to cut the previous arcs at C and D.

4. Draw line CD. This line CD is the required perpendicular bisector of $\overline{XY}$.

5. Mark any point P on the bisector CD.

6. Let CD meet $\overline{XY}$ at point M.

(i) On measuring PX and PY with the help of a ruler or divider, we find that PX = PY.

Hence, yes, PX = PY.

(ii) Since M lies on the perpendicular bisector of $\overline{XY}$ and M is the mid-point of $\overline{XY}$, therefore, $MX = MY$.

Hence, the lengths MX and MY are equal.