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# Draw a line segment of length $ 12.8 \mathrm{~cm} $. Using compasses, divide it into four equal parts. Verify by actual measurement.

**To do:**

We have to divide the line segment $12.8\ cm$ using compasses into four equal parts and verify by actual measurement.

**Solution:**

__Steps of construction:__

(i) Let us draw a line segment $\overline{XY}$ of length $12.8\ cm$.Now, with compasses take a measure greater than half of the length of $\overline{XY}$.

(ii) 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. 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.

(iii) Then, let's draw a line segment joining intersecting points of the arcs above and below the $\overline{XY}$ and name the point of intersection of the bisector with $\overline{XY}$ as C Therefore, C becomes the midpoint of $\overline{XY}$.

(iv) In a similar way take a measure greater than half of the length of $\overline{CB}$ with compasses. Now, by pointing the pointer of the compasses at point C and point B respectively. let's draw two arcs cutting each other above the line segment $\overline{XY}$.

(v) Similarly, by pointing the pointer of the compasses at point C and point B respectively. let's draw another two arcs cutting each other below the line segment $\overline{XY}$. Then, let's draw a line segment joining intersecting points of the arcs above and below the $\overline{XY}$ and name the point of intersection of the bisector with $\overline{XY}$ as E.

(vi) Therefore, E becomes the midpoint of $\overline{CY}$. In a similar way take a measure greater than half of the length of $\overline{AX}$ with compasses.

(vii) Now, by pointing the pointer of the compasses at point X and point C respectively. let's draw two arcs above the line segment cutting each other $\overline{XC}$. Similarly, by pointing the pointer of the compasses at point X and point C respectively. let's draw another two arcs cutting each other below the line segment $\overline{XY}$.

(ix) Then, let's draw a line segment joining intersecting points of the arcs above and below the $\overline{XY}$ and name the point of intersection of the bisector with $\overline{XY}$ as D.Therefore, D becomes the midpoint of $\overline{XC}$.

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