Question

select the correct answer.
which statement describes a reflection?
a. a reflection occurs when a point and its image are equidistant from a line on the opposite sides of the line and the line segment joining the two points is perpendicular to the line.
b. a reflection moves points a specified distance along a line perpendicular to a specified line.
c. a reflection occurs when an object moves in a circular arc around a point.
d. a reflection moves points a specified distance along a line parallel to a specified line.

Explanation:

• Option A:
• In a reflection, for every point \(P\) in the pre - image, its image \(P'\) has the property that the line of reflection \(l\) is the perpendicular bisector of the segment \(PP'\). That is, the distance from \(P\) to \(l\) is equal to the distance from \(P'\) to \(l\), and \(PP'\perp l\).
• Option B:
• Moving points a specified distance along a line perpendicular to a specified line is a translation (if the movement is in a straight - line, non - rotational, non - mirroring way). A reflection is a mirror - like transformation, not just a one - direction perpendicular movement.
• Option C:
• When an object moves in a circular arc around a point, it is a rotation. Rotation is a transformation where a figure is turned around a fixed point (the center of rotation).
• Option D:
• Moving points a specified distance along a line parallel to a specified line is also a translation. Translation slides a figure without rotating or reflecting it.

Answer:

A. A reflection occurs when a point and its image are equidistant from a line on the opposite sides of the line and the line segment joining the two points is perpendicular to the line.