Question
Draw a line segment of length $12.8\ cm.$ Using compasses, divide it into four equal parts. Verify by actual measurement.
✓
Answer
$1.$Draw a line segment $\overline{\text{XY}}$ of $12.8\ cm$.
$2.$Draw a circle, while taking point $X$ as centre and radius more than half of $XY.$
$3.$With same radius and taking centre as $Y,$ again draw arcs to cut the circle at $A$ and $B.$ Join $AB$ which
intersects $\overline{\text{XY}}$ at $M.$
$4.$Taking $X$ and $Y$ as centres, draw two circles with radius more than half of $\overline{\text{XY}}$.
$5.$With same radius and taking $M$ as centre, draw arcs to intersect these circles at $P, Q$ and $R, S.$
$6.$Join $PQ$ and $RS.$ These are intersecting $\overline{\text{XY}}$ at $T $ and $U.$
$7.$Now, $\overline{\text{XT}}=\overline{\text{TM}}=\overline{\text{MU}}=\overline{\text{UY}}$. These are $4$ equal parts of $\overline{\text{XY}}$.
By measuring these line segments with the help of ruler, we will find that each is of $3.2\ cm.$
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