Question

which sequence of transformations could map △abc to △xyz? a reflection across line m and a dilation a dilation by \\(\frac{1}{4}\\) and a reflection across line m a rotation about c and a dilation a dilation by \\(\frac{1}{4}\\) and a translation

Explanation:

Step1: Analyze Side Lengths

First, check the ratios of corresponding sides. For \( \triangle ABC \) and \( \triangle XYZ \):

• \( AC = 4 \), \( XZ = 1 \), ratio \( \frac{1}{4} \)
• \( AB = 6 \), \( XY = 1.5 \), ratio \( \frac{1.5}{6}=\frac{1}{4} \)
• \( BC = 5 \), \( YZ = 1.25 \), ratio \( \frac{1.25}{5}=\frac{1}{4} \)

So dilation factor is \( \frac{1}{4} \).

Step2: Check Orientation and Reflection

The triangles have angles in corresponding positions but reversed orientation (due to the angle markings' position), suggesting a reflection. Also, dilation by \( \frac{1}{4} \) first (or after) with reflection across line \( m \) matches. The option with dilation by \( \frac{1}{4} \) and reflection across line \( m \) fits.

Answer:

a dilation by \( \frac{1}{4} \) and a reflection across line \( m \)