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O Q 11. Line Segment FO below is used to begin a geometric construction. Which figure BEST represents the first step in constructing the perpendicular bisector of FQ? P.

O Q 11. Line Segment FO below is used to begin a geometric construction. Which figure BEST represents the first step in constructing the perpendicular bisector of FQ? P.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**11. Line Segment \( \overline{PQ} \) below is used to begin a geometric construction.** \[ \text{Diagram: A straight line labeled } P \text{ and } Q \text{ at each endpoint.} \] **Which figure BEST represents the first step in constructing the perpendicular bisector of \( \overline{PQ} \)?** - **Option A:** Two arcs intersecting each other with line segment \( \overline{PQ} \) in the center. Each arc is centered near endpoints \( P \) and \( Q \) and drawn above and below the line. - **Option B:** Line segment \( \overline{PQ} \) with two intersecting arcs below it, creating an "X" shape. - **Option C:** Line segment \( \overline{PQ} \) with two crossed lines below it, also creating an "X" shape but not as part of arcs. **Explanation of Diagram:** - The task is to identify which step correctly begins the construction of the perpendicular bisector of a line segment using a compass and straightedge method. The correct initial step involves creating arcs from each endpoint of the segment such that they intersect above and below the segment. This allows for the perpendicular bisector to be drawn through these intersections.
Transcribed Image Text:**11. Line Segment \( \overline{PQ} \) below is used to begin a geometric construction.** \[ \text{Diagram: A straight line labeled } P \text{ and } Q \text{ at each endpoint.} \] **Which figure BEST represents the first step in constructing the perpendicular bisector of \( \overline{PQ} \)?** - **Option A:** Two arcs intersecting each other with line segment \( \overline{PQ} \) in the center. Each arc is centered near endpoints \( P \) and \( Q \) and drawn above and below the line. - **Option B:** Line segment \( \overline{PQ} \) with two intersecting arcs below it, creating an "X" shape. - **Option C:** Line segment \( \overline{PQ} \) with two crossed lines below it, also creating an "X" shape but not as part of arcs. **Explanation of Diagram:** - The task is to identify which step correctly begins the construction of the perpendicular bisector of a line segment using a compass and straightedge method. The correct initial step involves creating arcs from each endpoint of the segment such that they intersect above and below the segment. This allows for the perpendicular bisector to be drawn through these intersections.
This image depicts a question about geometric lines and their intersections. It presents a multiple-choice question with several diagrams, each showing different configurations of a line segment labeled "PQ" and intersecting lines. 1. **Option A**: - Diagram shows a line segment labeled "PQ" with two arcs, each opening away from the points P and Q. - Below the line, there's a cross ('X') symbol. 2. **Option B**: - Diagram shows a straight line segment labeled "PQ". - Below the line, there are two cross ('X') symbols stacked vertically. 3. **Option C**: - Diagram shows a straight line segment labeled "PQ". - Below the line, there's a single cross ('X') symbol. 4. **Option D**: - Diagram shows a straight line segment labeled "PQ". - Below the line, there's a single cross ('X') symbol. Each diagram provides a visual representation related to lines and possible intersections to assess understanding of geometric principles.
Transcribed Image Text:This image depicts a question about geometric lines and their intersections. It presents a multiple-choice question with several diagrams, each showing different configurations of a line segment labeled "PQ" and intersecting lines. 1. **Option A**: - Diagram shows a line segment labeled "PQ" with two arcs, each opening away from the points P and Q. - Below the line, there's a cross ('X') symbol. 2. **Option B**: - Diagram shows a straight line segment labeled "PQ". - Below the line, there are two cross ('X') symbols stacked vertically. 3. **Option C**: - Diagram shows a straight line segment labeled "PQ". - Below the line, there's a single cross ('X') symbol. 4. **Option D**: - Diagram shows a straight line segment labeled "PQ". - Below the line, there's a single cross ('X') symbol. Each diagram provides a visual representation related to lines and possible intersections to assess understanding of geometric principles.
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