How Do You Construct A Perpendicular Bisector

Construction Of Perpendicular Bisector Of A Line Segment

A line which is perpendicular to a given line segment (AB) and divides it into two equal halves, i.e., AO = OB is called the perpendicular bisector of AB.

perpendicular-bisectorIn figure, XY is the perpendicular bisector of AB since AO = OB and ∠XOB = 90°.

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To draw a perpendicular bisector of a line segment

Construction: Draw the perpendicular bisector of a line segment AB = 5.5 cm using a scale and a pair of compasses.

  • Step 1: Draw a line segment AB of length 5.5 cm.

    perpendicular-bisector-construction
  • Step 2: Taking A as the centre and with any radius more than half of AB, draw an arc on both side of AB.

    perpendicular-bisector-construction-1
  • Step 3: Similarly, taking B as the centre and radius as in step 2, draw another arc on both side of AB intersecting the previous arcs at C and D.

    perpendicular-bisector-construction-2
  • Step 4: Join C and D crossing AB at O.

    Hence, CD is the required perpendicular bisector of AB.

Verification: Measure AO and OB. We find the measurement of AO = OB and also ∠COB = ∠COA = 90°.

Example 1:    Draw a line segment PQ of length 8.4 cm. Draw the perpendicular bisector of this line segment.

Solution:    We follow the following steps for constructing the perpendicular bisector of PQ.

Steps of Construction:

Step I: Draw a line segment PQ = 8.4 cm by using a ruler.

Step II: With P as centre and radius more than half of PQ, draw two arcs, one on each side of PQ.

Step III: With Q as centre and the same radius as in step II, draw arcs cutting the arcs drawn in the previous step at L and M respectively.

Step IV: Draw the line segment with L and M as end-points.

Perpendicular-Bisector-Of-A-Line-SegmentThe line segment LM is the required perpendicular bisector of PQ.

To draw a perpendicular at a point  on the line

Construction: Draw a perpendicular at a point on the line segment AB = 5.5 cm using a scale and a

pair of compasses.

Given: A line segment AB of length 5.5 cm and a 1 point P lying on it.

To construct: A line passing through P being perpendicular to AB

  • Step 1: Draw a line segment AB of length 5.5 cm and make a point P on it.

    perpendicular-bisector-construction-3
  • Step 2: Taking P as the centre and with any convenient radius, draw an arc cutting AB at X and Y.

    perpendicular-bisector-construction-4
  • Step 3: Taking X and Y as centres and with any suitable radius draw arcs cutting each other at Q.

    perpendicular-bisector-construction-5
  • Step 4: Join P and Q.

    Then PQ is perpendicular to AB passing through the point P.

    perpendicular-bisector-construction-6

To draw a perpendicular to a given line from a point lying outside the line

Construction: Draw a perpendicular from a point outside the line segment AB = 5.5 cm.

Given: A line segment AB of length 5.5 cm and a point Y lying outside the line.

To construct: A line passing through Y which is perpendicular to AB.

  • Step 1: Draw a line segment AB of length 5.5 cm and mark point Y outside the line segment AB.

    perpendicular-bisector-construction-7
  • Step 2: Taking Y as the centre and with any suitable radius, draw an arc cutting AB at C and D.

    perpendicular-bisector-construction-8
  • Step 3: Taking C and D as centres and with radius more than half of CD, draw arcs below AB intersecting each other at X.

    perpendicular-bisector-construction-9
  • Step 4: Join X and Y.

    Hence, XY is the required perpendicular to the line segment AB from point Y lying outside the line segment AB.

    perpendicular-bisector-construction-10
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