Q3.    Draw a line l and a point X on it. Through X, draw a line segment \overline{XY} perpendicular to l.

Now draw a perpendicular to \overline{XY} at Y. (use ruler and compasses)

Answers (1)

The steps of construction are as follows:

(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 the 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.

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