Question

Draw a line segment AB = 6 cm. Draw the perpendicular bisector of AB bisecting it at O. Further bisect OB at point P. Find the length of AO, OP and OB.​

Answer 1

Given:

Line segment AB = 6 cm

The perpendicular bisector of AB bisecting it at O

OB is bisected at point P

To find:

The length of AO, OP, and OB

Solution:

AB = 6cm

When AB is bisected at O, then OB and OA = 6/2

                                                                         = 3 cm

When OB is bisected at P, then OP and BP = 3/2

                                                                        = 1.5 cm

Hence, the length of AO, OP, and OB are 3 cm, 1.5 cm, and 3 cm respectively.

Construction:

• Step 1: Draw a line segment of length 6cm
• Step 2: Measure any radius more than half of the length AB and draw arcs above and below the line segment with A and B as the center.
• Step 3: Mark the points of intersection of arcs and join them. Mark O where the line meets the line segment AB.
• Step 4: Measure OA and OB.

• Step 5: Measure any radius more than half of the length OB and draw arcs above and below the line segment with O and B as the center.
• Step 6: Mark the point of intersection of arcs and join them. Mark P where the line meets the line segment.
• Step 7: Measure OP.

Answer 2

Drawn a line segment AB = 6 cm and drawn perpendicular bisector of AB bisecting AB at O and then drawn perpendicular bisector of OB , intersecting OB at P.

AO = 3 cm . OP = 1.5 cm , OB = 3 cm

Step 1: Draw a line segment AB = 6 cm

Step 2 : Using compass width more than half of AB draw arcs on both sides of AB taking A as center

Step 3 : Keeping compass width same and taking B as center draw arcs such that it intersects arcs drawn in previous steps at G and H

Step 4 : Join GH intersecting AB at O

AO = OB = AB/2  = 3 cm

Step 5 : Using compass width more than half of O draw arcs on both sides of OB taking O as center

Step 6 : Keeping compass width same and taking B as center draw arcs such that it intersects arcs drawn in previous steps at M and N

Step 4 : Join MN intersecting OB at P

OP = PB = OB/2  = 1.5 cm

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