Question

3. Draw the perpendicular bisector of a line segment
XY whose length is 11.2 cm.
(1) Take any point P on the right bisector drawn.
Examine whether PX=PY.
(2) If M is the midpoint of XY, what relation is
there between the lengths MX and XY?​

Answer 1

Relation is MX = MY = 5.6 cm

Step-by-step explanation:

• Steps of Construction -

1.) A line l is drawn with X point marked upon it.

2.) Take a measurement of length 11.2 cm with a ruler and compass.

3.) Draw an arc on 'l' line, with the pointed end at X and the same length of compass opened.

Hence, $\bar{XY}$ = 11.2 is required line.

• Now, Construction of Perpendicular Bisector.

Steps of Construction for Perpendicular Bisector-

1.) Taking $\bar{XY}$ as the same line segment.

2.) Taking a radius of more than half of 11.2 cm, draw two arcs both top and bottom of the line $\bar{XY}$ with X as the center.

3.) Taking the same radius as above in step 2, draw two similar arcs intersecting the above arcs at points C and D respectively but with Y as the center.  

• Joining CD gives the bisector of $\bar{XY}$.

1.) Now, P is being a point taken upon CD.

2. PX and PY are Joined.

3.) Measure the length of PX with the compass, check if the same opened mouth shows the same upon PY. Yes, that shows PX = PY

So, PX = PY.

• b) 'M' is marked as a point of intersection of lines XY and Cd.  

M is the needed midpoint or point of bisection

or MX = MY = 5.6 cm