Question

Draw a line segment $AB=8cm$. Mark a point $P$ on $AB$ such that $AP=4.5cm$. Draw a ray perpendicular to $AB$ at $P$ by using compasses.

Answer 1

Step 1: Construction of line segment

1. Mark any point in your exercise book and label it as $A$.

2. Place the ruler in such a way that the zero mark on the ruler coincides with $A$.

3. Now count 8 complete centimetres and mark a point corresponding to this division on the exercise book and mark as $B$.

4. Join $AB$.

So $AB$ is the required segment of length $8cm$.

Step 2: Construction of perpendicular

1. Mark a point $P$ on $AB$ such that $AP=4.5cm$.

2. With $P$ as centre and any suitable radius draw an arc to cut the line segment $AB$ at points $M$ and $N$.

3. With $M$ and $N$as centres and radius of more than half $MN$, draw two arcs to cut at $Q$.

4. Join $PQ$. Then, ray $PQ$ is the perpendicular to the line segment $AB$ at $P$.

Hence, ray $PQ$ is the perpendicular to the line segment $AB$ at $P$ drawn using compasses.