Chapter 10.2, Problem 2CE

To determine

To describe: the construction of midpoint of $\overline{BC}$ .

Explanation of Solution

Given information:

The given statement is “The midpoint of $\overline{BC}$ ”.

The procedure to construct midpoint of$\overline{BC}$:

• Consider the line segment $\overline{BC}$ .
• Choose a radius greater than $\frac{1}{2}\overline{BC}$ .
• Using the above radius and B as centre draw two arcs above and below the line $\overline{BC}$ .
• Using the same radius and C as centre draw two arcs above and below the line $\overline{BC}$ .
• Label the intersecting the points as $X\&Y$ .
• Observe $\overline{XY}$ is the perpendicular bisector of $\overline{BC}$ .
• The intersection point of $\overline{XY}\&\overline{BC}$ is the midpoint of $\overline{BC}$

The construction is shown below.

  

Hence, the construction of midpoint of $\overline{BC}$ is described.