Question

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 midpoint of $XY$, what can you say about the lengths $MX\&XY$ ?

Answer 1

Solution:

Steps of construction:

(1) Draw a line segment $\overline{XY}$ of $10.3$ cm

(2) Consider point$X$ as Centre and draw a circle by using compasses. The radius of circle should be more than half the length of $\overline{XY}$ .

(3) Now considering Y as Centre, draw another circle using compasses with the same radius as before. Let it cut at previous circle at points A and B

(4) Join AB. Here $\overline{AB}$ is the axis of symmetry.

(a) Take any point P on $\overline{AB}$ .We may observe that the measure of lengths of PX and PY are same . $\overline{AB}$ being the axis of symmetry, any point lying on $\overline{AB}$ will be at same distance from the both ends of $\overline{XY}$ .

(b) M is the midpoint of $\overline{XY}$ . Perpendicular bisector $\overline{AB}$ will be passing through point M. Hence length of $\overline{XY}$ is double of $\overline{MX}$

Hence, $2MX=XY$.