Question

consider the transformation. which statement about the transformation is true? it is isometric because the side lengths remained the same. it is isometric because all angle measures remained the same. it is not isometric because the side lengths did not remain the same. it is not isometric because the angle measures did not remain the same.

Explanation:

Step1: Recall the definition of isometric transformation

An isometric transformation (rigid transformation) preserves side - lengths and angle - measures.

Step2: Check side - lengths

In the top trapezoid, the non - parallel sides are of length \(2\) and the parallel sides are \(4\) and \(8\). In the bottom trapezoid, the non - parallel sides are of length \(4\) and the parallel sides are \(8\) and \(12\). The side - lengths have changed.

Step3: Analyze the options

• Option 1: Since side - lengths changed, it is not isometric. So, this option is wrong.
• Option 2: Even if angle measures remained the same (which they do in a non - isometric similarity transformation in some cases, but here we focus on side - lengths for isometry), because side - lengths changed, it is not isometric. So, this option is wrong.
• Option 3: Since side - lengths \(2

eq4\) and \(4
eq8\) (for non - parallel and parallel sides respectively), it is not isometric. This option is correct.

• Option 4: The problem with the transformation is the change in side - lengths (for isometry, side - lengths must be preserved). Angle measures can be preserved in non - isometric similarity transformations. So, this option is wrong.

Answer:

It is not isometric because the side lengths did not remain the same.