Draw a line l and a point X on it. Through X , draw a line segment X Y - perpendicular to l . Now draw a perpendicular to X Y - at Y . (use ruler and compasses)

Steps of construction: (i) Draw a line ‘ l ’ and mark a point X on it. (ii) Choose any convenient radius and with the pointed end of the compass at X , draw an arc intersecting the line ‘ l ’ at two points A and B . (iii) With A and B as centers and a radius greater than X A , draw two arcs, which intersect at a point, say C . (iv) Join X C and produce it to Y . Therefore, we obtain X Y perpendicular to ‘ l ’. (v) Choose any convenient radius and with the pointed end of the compass at Y , draw an arc intersecting X Y at two points P and Q . (vi) With P and Q as centers and radius greater than Y P , draw two arcs which intersect each other at a point say Z . (vii) Join Y Z . Therefore, we obtain Y Z perpendicular to X Y at Y .

Draw A B - of length 7.3 c m and find its axis of symmetry.

Axis of symmetry of line segment A B - will be the perpendicular bisector of A B - . So, we need to construct the perpendicular bisector of A B . Steps of construction: (i) Draw a line segment A B - = 7.3 c m using ruler. (ii) With A as the center and radius more than half of A B - , draw arcs above and below the line segment A B - . (iii) With B as the center and radius same as in step (ii), draw arcs above and below the line segment A B - . (iv) Name the point of intersection above the line segment as C and the point of intersection below the line segment as D . (v) Join C and D . Therefore, C D is the axis of symmetry of the line segment A B .

Draw the perpendicular bisector of X Y - whose length is 10.3 c m . Take any point P on the bisector drawn. Examine whether P X = P Y .

Steps of construction: (i) Draw a line l and mark a point X on it. (ii) Using a compass and ruler, cut an arc of 10 . 3 cm on the line. The point of intersection will be Y. So, we obtain X Y - = 10.3 c m (iii) With X as the center and radius more than half of X Y - , draw arcs above and below the line segment X Y - . (iv) With Y as the center and radius same as in step (iii), draw arcs above and below the line segment X Y - . (v) Name the point of intersection above the line segment as C and the point of intersection below the line segment as D . (vi) Join C and D . (vii) C D is the required perpendicular bisector of X Y - . Now: Take any point P on the bisector drawn. With the help of divider we can check that P X - = P Y - .

Draw the perpendicular bisector of X Y - whose length is 10.3 c m . If M is the mid-point of X Y - , what can you say about the lengths M X and X Y ?

Steps of construction: (i) Draw a line l and mark a point X on it. (ii) Using a compass and ruler, cut an arc of 10 . 3 cm on the line. The point of intersection will be Y . So, we obtain X Y - = 10.3 c m (iii) With X as the center and radius more than half of X Y - , draw arcs above and below the line segment X Y - . (iv) With Y as the center and radius same as in step (iii), draw arcs above and below the line segment X Y - . (v) Name the point of intersection above the line segment as C and the point of intersection below the line segment as D . (vi) Join C and D . (vii) C D is the required perpendicular bisector of X Y - . Now: If M is the mid-point of X Y - , it divides X Y - into two halves. Therefore, M X - = 1 2 X Y - = M Y -