Question

Draw a line PQ. Take a point R on it. Draw a line perpendicular to PQ and passing through R. (Using ruler and compasses)

Answer 1

Hint: This question is based on Geometry construction and we have to draw two lines perpendicular to each other using ruler and compasses.

Complete step-by-step answer:
This question is based on Geometry construction and we have to draw two lines perpendicular to each other using ruler and compasses.
Given:

The step by step construction is given by-
i) First draw a line PQ using the ruler and assume a point R on the line PQ.
ii) Now taking point R as the Centre and considering any convenient value of radius draw two arcs on the line PQ on the left and the right side of the point R using the compass.
iii) Name these two intersection points of the arcs A and B respectively.
iv) Now taking a radius greater than either RA or RB and considering A and B as the Centre draws two arcs. The point at which the arcs intersects each other name it as S.
v) Now join the RS and extend this line in both directions. This line say XY is perpendicular to the line PQ.
Therefore, we have obtained a line XY which is perpendicular to the line PQ and passes through point R.

Note: The alternate method of drawing the perpendicular line is by using a protractor. Take point R as a Centre and draw a line at $90^\circ $ from the line PQ. Extend this line to the both sides and name it as XY. Hence, we have constructed a line XY in such a way that $XY \bot PQ$ and the line XY passes through the point R.