Question

1. draw the image of quadrilateral abcd when translated by the directed line segment v. label the image of a as a, the image of b as b, the image of c as c and the image of d as d.
2. which statement is true about a translation?

a. a translation takes a line to a parallel line or itself.
b. a translation takes a line to a perpendicular line.
c. a translation requires a center of translation.
d. a translation requires a line of translation.

1. select all the points that stay in the same location after bei

Explanation:

• Option A: In a translation, a line is moved without rotation or reflection. If the line is not on the translation path (i.e., not the same line as the translation vector's direction in a non - zero translation), it will be parallel to its image. If the line is in the direction of the translation vector (in a non - zero translation, but if the translation is zero, which is a special case of identity transformation), it can map to itself.
• Option B: A translation is a rigid transformation that preserves orientation. Since it preserves orientation, a line and its image cannot be perpendicular (a rotation of \(90^{\circ}\) would be needed for perpendicularity, which is not a translation operation).
• Option C: A translation does not require a center. Rotations require a center of rotation.
• Option D: A translation is defined by a vector (magnitude and direction), not by a line of translation (reflections require a line of reflection).

Answer:

A. A translation takes a line to a parallel line or itself.