Question

select the correct answer from each drop - down menu. consider triangle abc shown on the graph. side lengths and angle measures will be preserved when △abc is side lengths are not preserved when △abc is reflected across the y - axis, dilated by a scale factor of 1/2, stretched vertically by a scale factor of 2

Explanation:

Step1: Analyze reflection across y - axis

Reflection across the y - axis is a rigid transformation. In a rigid transformation, the shape and size of the figure remain the same, which means side lengths and angle measures are preserved. So reflection across the y - axis preserves side lengths and angle measures.

Step2: Analyze dilation by scale factor 1/2

Dilation is a non - rigid transformation (similarity transformation) when the scale factor is not 1. When we dilate a triangle with a scale factor of \( \frac{1}{2} \), the side lengths are multiplied by \( \frac{1}{2} \), so side lengths are not preserved, but angle measures are preserved (since dilation preserves the shape, just changes the size).

Step3: Analyze vertical stretch by scale factor 2

A vertical stretch by a scale factor of 2 is a non - rigid transformation. It changes the vertical lengths of the sides. For example, the vertical side (if any) or the slant sides' vertical components will be stretched, so side lengths are not preserved, and it also distorts the shape in a way that angle measures may not be preserved. But for the first blank (side lengths and angle measures preserved), the only transformation among the options that is rigid is reflection across the y - axis. For the second blank (side lengths not preserved), both dilation by scale factor 1/2 and vertical stretch by scale factor 2 are non - rigid, but let's focus on the first part.

Answer:

For the first drop - down (side lengths and angle measures will be preserved when \( \triangle ABC \) is): reflected across the y - axis
For the second drop - down (side lengths are not preserved when \( \triangle ABC \) is): dilated by a scale factor of 1/2 (or stretched vertically by a scale factor of 2, but since the first part is reflection, the second part can be either of the non - rigid ones. If we take the first non - rigid option from the list, it's dilated by a scale factor of 1/2)