Question
Draw a line segment of length $12.8\ cm,$ Using compasses, divide it into four equal parts. Verify by actual measurement.
✓
Answer
$i.\ $Draw a line segment $\overline {A B}$ of length $12.8\ cm.$
$ii.\ $With A as centre, using compasses, draw an arc. The radius of this arc should be more than half of the length of $\overline {A B}$ .
$iii.\ $With the same radius and with $B$ as centre, draw another arc using compasses. Let it cut the previous arc at $C$ and $D.$
$iv.\ $Join $\overline {C D}$ . It cuts $\overline {A B}$ at $E.$ Then $\overline {C D}$ is the perpendicular bisector of the line segment $\overline {A B}$.
$v.\ $With $A$ as centre, using compasses, draw an arc. The radius of this arc should be more than half of the length of $AE.$
$vi.\ $With the same radius and with $E$ as centre, draw another arc using compasses. Let it cut the previous arc at $F$ and $G.$
$vii.\ $Join $\overline {F G}$ . It cuts $\overline {A E}$ at $H.$ Then $\overline {F G}$ is the perpendicular bisector of the line segment $\overline {A E}$ .
$viii.\ $With $E$ as centre, using compasses, draw an arc . The radius of this arc should be more than half of the length of $EB.$
$ix.\ $With the same radius and with $B$ as centre, draw another arc using compasses. Let it cut the previous arc at $I$ and $J.$
$x.\ $Join $\overline {I J}$. It cuts $\overline {E B}$ at $K.$ Then $\overline {I J}$ is the perpendicular bisector of the line segment $\overline {E B}$.
$xi.\ $Now, the points $H, E$ and $K$ divide $AB$ into four equal parts, i.e.,
$\overline{A H}=\overline{H E}=\overline{E K}=\overline{K B}$
By measurement,
$\overline{\mathrm{AH}}=\overline{\mathrm{HE}}=\overline{\mathrm{EK}}=\overline{\mathrm{KB}} = 3.2\ cm.$
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