To determine the slope of the dilated line [tex]\(\overline{X'Y'}\)[/tex], we need to understand how dilation affects various properties of geometric figures, particularly lines.
Dilation and Its Effect on a Line:
- Dilation is a transformation that resizes objects by a given scale factor from a specific point, known as the center of dilation.
- When a line segment is dilated with respect to the origin, the lengths of the segments change, but the orientation (i.e., the slope) remains the same.
Given the line segment [tex]\(\overline{XY}\)[/tex]:
- Original Slope [tex]\(m\)[/tex]: The slope of [tex]\(\overline{XY}\)[/tex] is given as [tex]\(m\)[/tex].
- Length: The actual length of [tex]\(\overline{XY}\)[/tex] is not directly specified but it is irrelevant to the slope.
Upon dilation by a scale factor of 1.3:
- The line segment [tex]\(\overline{XY}\)[/tex] is resized to form [tex]\(\overline{X'Y'}\)[/tex].
- Change in Length: The length of the new line segment [tex]\(\overline{X'Y'}\)[/tex] becomes 1.3 times the original length. However, the question does not ask about length but rather about the slope.
- Change in Slope: Dilation does not affect the slope of a line. This means the slope of [tex]\(\overline{X'Y'}\)[/tex] remains the same as the slope of [tex]\(\overline{XY}\)[/tex].
Therefore, the slope of [tex]\(\overline{X'Y'}\)[/tex] remains [tex]\(m\)[/tex].
Hence, the correct answer is:
[tex]\[ \text{D. } m \][/tex]
