question_answer 1)

Draw a line \[l\] and a point X on it. Through X, draw a line segment \[{{l}_{4}}\] perpendicular to \[l\]. Now, draw a perpendicular to \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\] at Y. (use ruler and compasses)

Answer:

                To draw \[{{l}_{4}}\] perpendicular on \[l\] and then a perpendicular to \[{{l}_{1}}\] at Y, we use the following steps: Step I Firstly, draw a line I and take point X on it. Step II With X as centre and a convenient radius, draw an arc intersecting the line \[l\] at two points A and B. Step III With A and B as centres and radius greater than \[{{l}_{1}},{{l}_{2}},{{l}_{3}},{{l}_{4}},{{l}_{5}}\] draw two arcs, which cut each other at C. Step IV Join \[{{l}_{6}}\] and produce it to Y. Then, \[{{l}_{1}},{{l}_{2}},{{l}_{3}},{{l}_{4}},{{l}_{5}}\] is perpendicular to \[l\]. Step V With y as centre and a convenient radius, draw an arc intersecting \[{{l}_{6}}\] at two points E and D. Step VI With E and D as centres and a radius greater than \[{{l}_{1}},{{l}_{2}},{{l}_{3}},{{l}_{4}}\] draw two arcs, which cut each other at F. Step VII Join \[{{l}_{5}}\] then YF is perpendicular to \[{{l}_{1}},{{l}_{2}}\] at Y. i.e. \[{{l}_{3}}\]and\[{{l}_{1}},{{l}_{2}},{{l}_{3}}\]