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Question
Draw a line l and a point X on it. Through X, draw a line segment ¯¯¯¯¯¯¯¯¯XY perpendicular to l. Now draw a perpendicular to ¯¯¯¯¯¯¯¯¯XY to Y. (use ruler and compasses)
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Solution
Steps of construction:
(i) Draw a line 'l' and take point X on it.
(ii) With X as the centre and a convenient radius, draw an arc intersecting the line 'l' at two points A and B.
(iii) With A and B as centres and a radius greater than XA, draw two arcs, which cut each other at C.
(iv) Join AC and produce it to Y. Then XY is perpendicular to 'l'.
(v) With Y as centre and a convenient radius, draw an arc intersecting XY at two points C and D.
(vi) With C and D as centres and radius greater than YD, draw two arcs which cut each other at F.
(vii) Join YF, then YF is perpendicular to XY at Y.
Hence, we get the figure as shown below:
Steps of construction:
(i) Draw a line 'l' and take point X on it.
(ii) With X as the centre and a convenient radius, draw an arc intersecting the line 'l' at two points A and B.
(iii) With A and B as centres and a radius greater than XA, draw two arcs, which cut each other at C.
(iv) Join AC and produce it to Y. Then XY is perpendicular to 'l'.
(v) With Y as centre and a convenient radius, draw an arc intersecting XY at two points C and D.
(vi) With C and D as centres and radius greater than YD, draw two arcs which cut each other at F.
(vii) Join YF, then YF is perpendicular to XY at Y.
Hence, we get the figure as shown below:
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