Question: What are the four steps, in order, to construct the perpendicular bisector of $PQ$?
Center the compass at point $P$ and draw a circle AND center the compass at point $Q$ and draw a circle.
Use your straightedge to draw a line through the intersections of the circles.
Identify the intersections of the two circles.
Expand your compass to equal the length of $PQ$.
1. **State the problem:** We need to construct the perpendicular bisector of the line segment $PQ$.
2. **Step 1:** Expand your compass to equal the length of $PQ$. This means setting the compass width to the distance between points $P$ and $Q$.
3. **Step 2:** Center the compass at point $P$ and draw a circle. Then, center the compass at point $Q$ and draw another circle with the same radius. These two circles will intersect at two points.
4. **Step 3:** Identify the intersections of the two circles. These intersection points are equidistant from $P$ and $Q$.
5. **Step 4:** Use your straightedge to draw a line through the intersections of the circles. This line is the perpendicular bisector of $PQ$, meaning it divides $PQ$ into two equal parts at a right angle.
**Final answer:** The correct order of steps is:
1. Expand your compass to equal the length of $PQ$.
2. Center the compass at point $P$ and draw a circle AND center the compass at point $Q$ and draw a circle.
3. Identify the intersections of the two circles.
4. Use your straightedge to draw a line through the intersections of the circles.