Question

1. which statement is true about a translation?
2. a translation takes a line to a parallel line or itself.
3. a translation takes a line to a perpendicular line.
4. a translation requires a center of translation.
5. a translation requires a line of translation.

Explanation:

Step1: Recall the properties of translation

Translation is a transformation that slides every point of a figure or space by the same distance in a given direction.

Step2: Analyze each option

• Option 1:

When a line is translated, if the line is not vertical (in a non - vertical direction of translation), the translated line is parallel to the original line. If the translation is in a direction along the line (for a straight line), the line is mapped to itself.

• Option 2:

Translation does not change the slope of a line (in a coordinate - plane interpretation). If two lines are perpendicular, their slopes \(m_1\) and \(m_2\) satisfy \(m_1\times m_2=- 1\). Since translation preserves the slope of a line (or direction in a non - coordinate geometric sense), a translation does not take a line to a perpendicular line.

• Option 3:

A rotation requires a center of rotation. A translation is determined by a vector (a direction and a magnitude), not a center.

• Option 4:

A reflection requires a line of reflection. A translation is determined by a translation vector (a displacement vector), not a line of translation.

Answer:

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