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Draw the perpendicular bisector of XY whose length is 10.3 cm.
(a) Take any point P on the bisector drawn. Examine whether PX = PY.
(b) If M is the mid point of XY, what can you say about the lengths MX and XY?

Solution:

Let's follow the steps below to draw a perpendicular bisector.

Step 1: Draw a line segment XY of length 10.3 cm.

Draw the perpendicular bisector of XY whose length is 10.3 cm. (a) Take any point P on the bisector drawn. Examine whether PX = PY. (b) If M is the mid point of XY, what can you say about the lengths MX and XY?

Step 2: Taking X and Y as centers, mark two arcs that intersect each other at R and S.

Step 3: Join RS to construct a perpendicular bisector of the given line segment that meets XY at M.

Draw the perpendicular bisector of XY whose length is 10.3 cm. (a) Take any point P on the bisector drawn. Examine whether PX = PY. (b) If M is the mid point of XY, what can you say about the lengths MX and XY?

Thus, RS is the perpendicular bisector of XY.

a) Take a point P on RS and join PX and PY.

Draw the perpendicular bisector of XY whose length is 10.3 cm. (a) Take any point P on the bisector drawn. Examine whether PX = PY. (b) If M is the mid point of XY, what can you say about the lengths MX and XY?

On measuring PX and PY, we see that PX = PY as RS is the axis of symmetry. Any point on RS will be equidistant from XY.

b) If M is the midpoint of XY, MX = MY as RS also bisects the line segment meeting XY at M. Thus, MX = MY = 1/ 2 XY

NCERT Solutions for Class 6 Maths Chapter 14 Exercise 14.5 Question 3