Question
Identify which diagram represents a step in constructing a perpendicular line that is not a perpendicular bisector.(1 point)
Responses
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.
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.
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 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.
Responses
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.
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.
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 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.
Answers
GPT-4o mini
To identify a step in constructing a perpendicular line that is not a perpendicular bisector, we need to analyze each described scenario:
1. **First diagram (A)**: The compass is on point A, with the pencil approximately two-thirds of the way along line segment AB. This action could be part of constructing a perpendicular line, but it seems it may lead toward a perpendicular bisector since it starts from endpoint A.
2. **Second diagram (B)**: Here, the compass needle is on point B, with the pencil placed about two-thirds of the way along segment AB. This action does not suggest a perpendicular bisector and may be aimed at constructing a perpendicular line from point B.
3. **Third diagram (C)**: Arcs bisected by AB intersect at points C and D, and a line drawn through C and D forms a right angle at the midpoint M. This clearly represents a construction of a perpendicular bisector because it utilizes the midpoint of AB.
4. **Fourth diagram (D)**: A vertical line segment is shown that is perpendicular to segment XY, intersecting it about one-fourth of the distance between X and Y. This construction is explicitly creating a perpendicular line at a point that is not the midpoint, and thus is not a perpendicular bisector.
Based on this analysis, the diagram that represents a step in constructing a perpendicular line that is not a perpendicular bisector is **the fourth diagram (D)**.
1. **First diagram (A)**: The compass is on point A, with the pencil approximately two-thirds of the way along line segment AB. This action could be part of constructing a perpendicular line, but it seems it may lead toward a perpendicular bisector since it starts from endpoint A.
2. **Second diagram (B)**: Here, the compass needle is on point B, with the pencil placed about two-thirds of the way along segment AB. This action does not suggest a perpendicular bisector and may be aimed at constructing a perpendicular line from point B.
3. **Third diagram (C)**: Arcs bisected by AB intersect at points C and D, and a line drawn through C and D forms a right angle at the midpoint M. This clearly represents a construction of a perpendicular bisector because it utilizes the midpoint of AB.
4. **Fourth diagram (D)**: A vertical line segment is shown that is perpendicular to segment XY, intersecting it about one-fourth of the distance between X and Y. This construction is explicitly creating a perpendicular line at a point that is not the midpoint, and thus is not a perpendicular bisector.
Based on this analysis, the diagram that represents a step in constructing a perpendicular line that is not a perpendicular bisector is **the fourth diagram (D)**.