Question

Draw any line segment $\overline{\text{AB}}$. Mark any point $M$ on it. Through $M,$ draw a perpendicular to $\overline{\text{AB}}$. $($use ruler and compasses$)$

Answer

$1.$Draw the given line segment $\overline{\text{AB}}$ and mark any point $M$ on it.

$2.$With $M$ as centre and a convenient radius, construct an arc intersecting the line segment $\overline{\text{AB}}$ at two points $C$ and $D.$

$3.$With $C$ and $D $ as centres and a radius greater than $CM$ construct two arcs. Let these are intersecting each other at $E.$

$4.$Join $EM.$ $\overline{\text{EM}}$ is perpendicular to $\overline{\text{AB}}$.

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