Question

Describe how you would construct each of the following:

The midpoint of $\overline{BC}$.

Short answer

The construction of midpoint of $\overline{BC}$ is described.

Step-by-step solution

Step 1. Given information.   

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

Step 2. Concept used.

Draw arc with radius greater than that side and joint the point of intersection.

Step 3. Solution.

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:

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