Question
Use a compass and straightedge to construct a perpendicular bisector to start overline, R, S, end overline
RS
. Your final answer should be exactly one blue line (not a line segment).
You must start your line segment at an existing point, arc, or line.
Answer
Attempt 2 out of 2
RS
. Your final answer should be exactly one blue line (not a line segment).
You must start your line segment at an existing point, arc, or line.
Answer
Attempt 2 out of 2
Answers
GPT-4o mini
To construct the perpendicular bisector of the line segment \( \overline{RS} \) using only a compass and straightedge, follow these steps:
1. **Draw Points**: Mark the endpoints of the line segment \( R \) and \( S \).
2. **Measure Segment Length**: Use the compass to measure the length of the segment \( \overline{RS} \).
3. **Draw Circles**:
- With the compass centered at point \( R \), draw a circle with a radius greater than half the length of \( \overline{RS} \) so that it intersects both sides of the line segment \( RS \).
- Without changing the width of the compass, center it at point \( S \) and draw a second circle around point \( S \).
4. **Find Intersections**: Mark the points where the circles intersect. Let's call the intersection points \( A \) and \( B \).
5. **Draw the Perpendicular Bisector**:
- Use the straightedge to draw a line through points \( A \) and \( B \). This line is the perpendicular bisector of \( \overline{RS} \).
This line divides the segment \( \overline{RS} \) into two equal parts at a right angle, completing the construction of the perpendicular bisector.
To represent this as an answer with only one blue line:
- Draw the line that results from connecting \( A \) and \( B \).
You can represent your answer in a visual format, ensuring the perpendicular bisector is clear and distinct as a straight line intersecting \( R \) and \( S \) orthogonally.
1. **Draw Points**: Mark the endpoints of the line segment \( R \) and \( S \).
2. **Measure Segment Length**: Use the compass to measure the length of the segment \( \overline{RS} \).
3. **Draw Circles**:
- With the compass centered at point \( R \), draw a circle with a radius greater than half the length of \( \overline{RS} \) so that it intersects both sides of the line segment \( RS \).
- Without changing the width of the compass, center it at point \( S \) and draw a second circle around point \( S \).
4. **Find Intersections**: Mark the points where the circles intersect. Let's call the intersection points \( A \) and \( B \).
5. **Draw the Perpendicular Bisector**:
- Use the straightedge to draw a line through points \( A \) and \( B \). This line is the perpendicular bisector of \( \overline{RS} \).
This line divides the segment \( \overline{RS} \) into two equal parts at a right angle, completing the construction of the perpendicular bisector.
To represent this as an answer with only one blue line:
- Draw the line that results from connecting \( A \) and \( B \).
You can represent your answer in a visual format, ensuring the perpendicular bisector is clear and distinct as a straight line intersecting \( R \) and \( S \) orthogonally.