Question

1. in the diagram below, line m is parallel to line n. figure 2 is the image of figure 1 after a reflection over line m. figure 3 is the image of figure 2 after a reflection over line n. which single transformation would carry figure 1 onto figure 3? a) a reflection b) a dilation c) a rotation d) a translation

Explanation:

Step1: Analyze the properties of each transformation

• Reflection: Flips a figure over a line. Two reflections over parallel lines do not result in a single reflection.
• Dilation: Changes the size of a figure. The figures here are congruent (same size and shape), so dilation is not applicable.
• Rotation: Changes the orientation of a figure around a point. But in this case, the transformation is not a rotation.
• Translation: Slides a figure without rotating or resizing. When you reflect a figure over two parallel lines (\(m\) and \(n\)), the composition of these two reflections (since \(m\parallel n\)) is equivalent to a translation. The distance of the translation is twice the distance between the two parallel lines \(m\) and \(n\).

Answer:

D. a translation