Question

triangle abc was reflected over line m, then dilated by a scale factor between 0 and 1. which diagram illustrates these transformations?

Explanation:

Step1: Understand Reflection

Reflection over a line \(m\) changes the position of the triangle with respect to the line \(m\) such that the line \(m\) is the perpendicular bisector of the line - segments joining corresponding vertices of the original and reflected triangle.

Step2: Understand Dilation with scale factor \(0 < k<1\)

Dilation with a scale factor \(k\) (where \(0 < k<1\)) reduces the size of the triangle. The angles of the triangle remain the same (since dilation is a similarity transformation), but the side - lengths are multiplied by \(k\).

Looking at the first diagram:

• The reflection over line \(m\) is correctly represented (the orientation of the triangle with respect to line \(m\) is that of a mirror - image).
• The dilated triangle \(A''B''C''\) is smaller than the reflected triangle (which is consistent with a scale factor between \(0\) and \(1\)) and the angles are preserved.

In the second diagram:

• The reflection is not properly represented (the orientation of the triangle with respect to line \(m\) is incorrect for a reflection).

Answer:

The first diagram (the one with triangle \(ABC\) on the left of line \(m\), a reflected and then dilated triangle \(A''B''C''\) on the right of line \(m\) with smaller size and preserved angles) is the correct illustration.