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Identify which diagram represents a step in constructing a perpendicular line that is not a perpendicular bisector.(1 point)

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A line segment has 2 end points. The left end point is A, and the right is B. A geometric compass is shown with the compass needle on point A and the pencil of the compass placed about two thirds of the way along line segment A B.
Image with alt text: A line segment has 2 end points. The left end point is A, and the right is B. A geometric compass is shown with the compass needle on point A and the pencil of the compass placed about two thirds of the way along line segment A B.

Two arcs are bisected by line segment A B. The arcs intersect at points C above the midpoint of A B and D below the midpoint of A B. A line is drawn from point C to D through the midpoint, M, of A B forming a right angle.
Image with alt text: Two arcs are bisected by line segment A B. The arcs intersect at points C above the midpoint of A B and D below the midpoint of A B. A line is drawn from point C to D through the midpoint, M, of A B forming a right angle.

A line segment has 2 end points labeled A and B. A compass has its needle on the right end point, B, and its pencil is placed about two thirds of the way along line segment.
Image with alt text: A line segment has 2 end points labeled A and B. A compass has its needle on the right end point, B, and its pencil is placed about two thirds of the way along line segment.

A solid line segment with two end points, X and Y, is shown. A dashed vertical line segment is also shown perpendicular to the segment X Y, intersecting it approximately one fourth of the distance between X and Y.

1 answer

To identify which diagram represents a step in constructing a perpendicular line that is not a perpendicular bisector, we need to understand the characteristics of both types of construction.

  1. Perpendicular bisector: This specifically involves finding the midpoint of a line segment and drawing a line that is perpendicular to the segment at that midpoint.

  2. Perpendicular line (not bisector): This simply entails drawing a line perpendicular to an existing line segment without necessarily bisecting it.

Now let's analyze the diagrams:

  • First Diagram: A compass is shown with its needle on point A while the pencil points two-thirds of the way along segment AB. This does not indicate a construction step for either a perpendicular bisector or a perpendicular line since it lacks context about determining a perpendicular relationship.

  • Second Diagram: This shows two arcs intersecting at points C and D above and below the midpoint M of AB, with a line drawn through C and D, which indicates the construction of a perpendicular bisector since it bisects segment AB at its midpoint.

  • Third Diagram: A compass is on point B, with the pencil placed two-thirds of the way along segment AB. Like the first, this does not illustrate a specific step toward creating a perpendicular line.

  • Fourth Diagram: This shows a dashed vertical line that is perpendicular to segment XY and intersects it about one fourth of the distance between points X and Y. This represents the construction of a perpendicular line that is not a bisector since it does not bisect the segment.

Conclusion: The fourth diagram, which shows a dashed vertical line segment perpendicular to segment XY, represents a step in constructing a perpendicular line that is not a perpendicular bisector.