Question

Draw a line segment $\overline{PQ}$ of length $$6.5cm$$. Construct the perpendicular bisector of $\overline{PQ}$ using a ruler and compasses. Write the steps of construction.

Answer 1

Hint: If a line cuts a line segment in equal parts vertically at ${90}^{\circ }$, then that vertical line is called perpendicular bisector of line segment as shown in figure below:

To construct a perpendicular bisector, first draw a line segment PQ with the help of a ruler. Taking P and Q as centre with the same radius cut off arcs on both sides i.e. above and below the line segment with the help of a compass. Then join the points R and S as shown in above figure.

Complete step-by-step answer:
With the help of a ruler draw a line segment PQ, say$$PQ=6cm$$.

Taking P as centre and radius more than half PQ and mark an arc with the help of compass on both sides i.e. above and below the line segment PQ.

Taking Q as centre and the same radius and mark an arc with the help of compass on both sides i.e. above and below the line segment PQ.

Taking Q as centre and the same radius and mark an arc with the help of compass on both sides i.e. above and below the line segment PQ.

Join PQ, cutting PQ at O. Then O bisects RS.

We have successfully constructed the perpendicular bisector of PQ i.e. RS.
You can also check if the measure of $$PO=OQ=3.25cm$$ & $\mathrm{\angle }POR=\mathrm{\angle }QOR={90}^{\circ }$. If it satisfies these parameters then the construction is accurate.
Therefore, RS is the perpendicular bisector of PQ.

Note:1. You can draw a rough sketch of the construction so you can get the clear idea of the construction.
2.Don’t change the radius while making the arc from both sides.
3.While measuring the angle starts from zero degrees.
4.Try to measure with greater accuracy.