Question

1. determine if the following statement is sometimes, always or never true. justify your reasoning! translating and reflecting will produce the same image as reflecting and then translating.

Explanation:

Step1: Consider order - dependent cases

If we reflect a figure over a line and then translate it, and then consider the case where we first translate and then reflect over the same line, the results can be different. For example, if we have a figure near the line of reflection and translate it far away first and then reflect, it will be in a different position compared to reflecting first and then translating.

Step2: Consider special cases

If the translation vector is parallel to the line of reflection, then translating and then reflecting will produce the same image as reflecting and then translating. So the statement is sometimes true.

Answer:

Sometimes