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In the following figure, draw a perpendicular through point P to the line segment AB.

Last updated date: 13th Jul 2024
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Hint: To draw a perpendicular through point P to the line segment, we have to draw an arc of suitable radius with P as the centre, which cuts the line segment AB at points X and Y. Then, with X and Y as centres and radius more than half of XY, we have to draw an arc from point X and point Y that intersect at point Q. Lastly, we have to join points P and Q. The line segment PQ intersects the line segment AB at O.

Complete step-by-step solution:
We have to draw a perpendicular through point P to the line segment AB. Firstly, we have to draw an arc of suitable radius with P as the centre, that cuts the line segment AB at points X and Y. This is shown in the figure below.

Now, with X and Y as centres and radius more than half of XY, we have to draw an arc from point X and point Y that intersect at point Q. We will obtain a figure as shown below.

Finally, we have to join points P and Q. This line segment PQ intersects the line segment AB at O. We will get the required perpendicular line PQ as shown below.

Thus, we have constructed a perpendicular through point P to the line segment AB.

Note: Students have a chance of taking the radius of the arcs to be drawn from X and Y as less than half of the length of the line segment XY. This will lead to improper construction of the required perpendicular. Students must note that the perpendicular PQ to the line segment AB creates angles $\angle POX$ and $\angle POY$ , each of $90{}^\circ$ .