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

Question

Responses

a. 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.

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.

c. 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.

d. 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.

Answer 1

To identify which diagram represents a step in constructing a perpendicular line that is not a perpendicular bisector, we need to understand what each of the options describes.

a. This diagram shows a vertical line segment that is perpendicular to the line segment XY and intersects it at a point that is not the midpoint, suggesting that it is constructing a perpendicular line. This fits the criteria.

b. This represents the construction of a perpendicular bisector, as it involves creating two arcs to find the midpoint (M) of AB and drawing a line through that midpoint, forming right angles with AB.

c. This diagram is ambiguous but suggests a compass is being used at point B to create an arc above the line segment. It is not clear that this forms a perpendicular line to XY.

d. This diagram indicates using the compass at point A to create an arc, again not indicating the creation of a perpendicular line.

Among these options, b clearly describes a step to construct a perpendicular bisector, while a describes a step to construct a perpendicular line. Therefore, the answer is that a is the step representing a perpendicular line that is not a perpendicular bisector.

The correct option that illustrates a construction of a perpendicular line (not a bisector) is a.