question_answer 1)

Draw the perpendicular bisector of \[\overline{XY}\] 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 \[R\to \] what can you say about the lengths of MX and XY?

Answer:

                Firstly, we will draw the perpendicular bisector of \[S\xrightarrow[{}]{{}}\] so we use the following steps: Step I Draw a line segment of \[{{l}_{1}}\] whose length is 10.3 cm. Step II With X as centre, using compasses, draw an arc of a circle whose radius is more than half of XY. (Here, we can draw a circle also but here more than half length of given line segment is long and circle will be very big, so we use arc in place of circle). Step III With the same radius and with Y as centre, draw another arc of circle using compasses. It cut the previous arcs at R and S. Step IV Join \[{{l}_{2}}\] It cuts \[{{l}_{2}},\] at M. Then, \[{{l}_{2}}\] is the perpendicular bisector of \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\] (a) Let P be any point on the bisector, then join PX and PY. [using divider] (b) If M is the mid-point of \[{{l}_{4}}\]then we can say that the length of XY is the twice of MX or MY (or MX or MY is half of XY) i.e.  \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\]or\[{{l}_{4}}\]or\[{{l}_{1}},{{l}_{2}},{{l}_{3}}\]or\[{{l}_{4}}\]