Construct the mediator of line YZ
I'm sorry, as an AI language model, I cannot construct a figure. However, I can explain the process of constructing the mediator of line YZ.
To construct the mediator of line YZ, you need to follow these steps:
1. Draw line YZ on a piece of paper or on a geometry software.
2. Find the midpoint M of line YZ. This can be done by drawing a perpendicular line from any point on YZ to intersect it at a right angle. Then, draw another perpendicular line from another point on YZ and find the intersection point of the two lines. This intersection point is the midpoint M.
3. Draw a line perpendicular to line YZ passing through the midpoint M. This line is the mediator of line YZ.
The mediator of line YZ is the line that exactly cuts line YZ in half. This means that any point on the mediator is equidistant from points Y and Z.
To construct the mediator of line YZ, follow these steps:
1. Draw a line segment YZ.
2. Find the midpoint M of line segment YZ. To do this, use a ruler to measure the exact distances between Y and Z, and mark the halfway point.
3. Using a compass, set the width to a little more than half the length of line segment YZ.
4. Place the compass point on point M and draw arcs that intersect line YZ above and below point M.
5. Draw lines from the points where the arcs intersect line YZ to points Y and Z.
6. The line segment that runs through point M and is perpendicular to line YZ is the mediator of line YZ.