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. 3. 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. 4. select all the points that stay in the same location after being reflected across line l. a. a b. b c. c d. d e. e

Explanation:

2.

Step1: Identify translation vector

Determine the direction and length of directed - line segment \(v\).

Step2: Translate each vertex

For vertex \(A\), move it along the direction of \(v\) by the length of \(v\) to get \(A'\). Repeat this process for \(B\) to get \(B'\), for \(C\) to get \(C'\) and for \(D\) to get \(D'\). Then connect \(A'\), \(B'\), \(C'\) and \(D'\) to form the translated quadrilateral.

3.

• Option A: By the definition of translation, a translation takes a line to a parallel line or itself. This is correct.
• Option B: A translation does not take a line to a perpendicular line. A rotation is used to get a perpendicular - related transformation.
• Option C: A rotation requires a center of rotation, not a translation.
• Option D: A translation requires a direction and a distance, not a line of translation (this is more related to reflection).

Points on the line of reflection stay in the same location after reflection. Points \(B\), \(C\) and \(E\) lie on line \(\ell\), so they will not change their position after reflection across line \(\ell\). Points \(A\) and \(D\) are not on the line \(\ell\), so they will move to new positions after reflection.

Answer:

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

4.