Question

look at the line segment graphed below.

graph of a line segment on a coordinate plane with endpoints at (2, 4) and (3, 12)

which statement is true regarding a translation of the line segment?

a. a translation of the line segment will always give an image parallel to the original line segment.

b. a translation of the line segment will always give an image with a proportional but different length than the original line segment.

c. a translation of the line segment may give an image with a slope opposite to that of the original line segment.

d. a translation of the line segment may give an image perpendicular to the original line segment.

Explanation:

Translation is a rigid transformation that shifts all points of a figure by the same vector. It preserves the direction and length of line segments. Thus, the image of a translated line segment remains parallel to the original (same slope, no change in direction), has equal length, and cannot be perpendicular or have an opposite slope. Only option A is correct.

Answer:

A. A translation of the line segment will always give an image parallel to the original line segment.