*Question 1:*

*A line segment \(\overline{PQ}\) .Point O is marked on it any where.On the point O perpendicular is drawn(by using compasses and ruler)*

Construction step:

(1)Keep O as midpoint and with some radius, an intersecting arc is drawn the line PQ at 2 points X and Y.

(ii) With X and Y as centers as well as radius more than OX, draw 2 arcs, they cut together at L.

(iii) Join LO. Then LO is perpendicular to PQ through O point.

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*Question 2:*

*A line segment is drawn AB. X as a point taken not on it By R, a perpendicular line is drawn*

*to AB. (Use set-square and ruler )*

** ****Answer: **

construction method:

(i)A set-square is placed on \(\overline{AB}\) such that one arm of its right angle aligns along \(\overline{AB}\)

(ii) A ruler is placed along the edge opposite to the right angle of the set-square.

(iii) Hold the ruler fixed. Set square slide the along the ruler till the point X touches set square’s other arm

(iv) Join OX along the edge through X meeting AB at O. Then XO is perpendicular to AB.

** **

*Question 3:*

* 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)*

*Answer:*

Construction step:

(1)Make a line ‘l’ and take point O on it.

(2)With O as centre and a certain radius, an arc is draw at intersecting the line ‘l’ at 2 points P and Q.

(3) With P and Q as centers and a radius greater than OP, draw 2 arcs, which cut each other at R.

(4) Join PR and produce it to M. Then OM is perpendicular to ‘l’

(5) With S as centre and a certain radius, draw an arc intersecting OM at two points R and S.

(6) With R and S as centers and radius greater than MS, draw 2 arcs and they cut each other at L.

(7) Join ML, then ML is perpendicular to OM at M