Question

Draw a line segment of the length of 8.6 centimeters. Bisect it and measure the length of each part.

Answer 1

Hint: We will draw a line segment of the given length. from the endpoints of this line segment we will draw arc at the top and below the line segments. The point at which the two arcs of these from these two points meet will be marked. Then we will draw a straight line joining the point of intersection above and below the line segment of 8.6 centimeter.


Complete step by step solution:
Given a line segment ML of length 8.6 centimeters.
Open the compass more than half of the distance between M and L, and scribe arcs of the same radius centered at M and L. It means with M as center and radius more than half of ML, we will draw arcs on both sides of ML.

With the same radius and L as center, we will draw arcs on both sides of ML, cutting the previous two arcs at O and K.
Calling the two points where these two arcs meet K and O we will draw a line segment between K and O which will bisect ML.
KO is the perpendicular bisector of the line segment ML. Call the point where KO intersects ML as P.
And since, P is at the center of line ML it is the midpoint of line ML.
Therefore ,We have
 \[\begin{align}
  & ML=MP+PL\,\,\text{ }\!\![\!\!\text{ as }p\text{ is the midpoint of line }ML\text{ }\!\!]\!\!\text{ } \\
 & MP=PL=\dfrac{ML}{2} \\
 & \therefore \,\text{the length of each part,} \\
 & MP=PL=\dfrac{8.6}{2}=4.3\text{ centimeter}\text{.} \\
 & \text{9}{{\text{0}}^{\circ }} \\
\end{align}\]

Note: The perpendicular bisector is cutting the line segment in two halves. Thus we name the point at which this bisector is cutting the line segment in two halves as the midpoint. And to verify the perpendicular bisector we need to check if the bisector is making \[\text{9}{{\text{0}}^{\circ }}\] with the line segment at the midpoint.
To yield an accurate perpendicular bisector we should use a sharpened pencil with a correct compass, otherwise while drawing the arcs we will make mistakes.