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5. [tex]\(\overline{XY}\)[/tex] is dilated by a scale factor of 1.3 with the origin as the center of dilation to create the image [tex]\(\overline{X'Y'}\)[/tex]. If the slope and length of [tex]\(\overline{XY}\)[/tex] are [tex]\(m\)[/tex] and [tex]\(I\)[/tex] respectively, what is the slope of [tex]\(\overline{X'Y'}\)[/tex]?

A. [tex]\(1.3 \times m\)[/tex]
B. [tex]\(1.3 \times 1\)[/tex]
C. [tex]\(1.3 \times (m + 1)\)[/tex]
D. [tex]\(m\)[/tex]

Sagot :

GinnyAnsweridn
To determine the slope of the line segment [tex]\(\overline{X'Y'}\)[/tex] after dilation, we need to understand the properties of dilation:

1. Understanding Dilation:
Dilation is a transformation that produces an image that is the same shape as the original, but is a different size. It involves a scale factor and a center of dilation.

2. Effect on Slope:
One key property of dilation is that it does not change the slope of the line. This is because dilation stretches or shrinks distances proportionally from the center of dilation, but it does not alter the angle between the line and the axes.

3. Given Information:
- The scale factor of dilation is [tex]\(1.3\)[/tex].
- The slope of [tex]\(\overline{XY}\)[/tex] is [tex]\(m\)[/tex].

Since dilation does not affect the slope of a line, the slope of the image line [tex]\(\overline{X'Y'}\)[/tex] will remain the same as that of [tex]\(\overline{XY}\)[/tex].

Therefore, the slope of [tex]\(\overline{X'Y'}\)[/tex] is:

[tex]\[ m \][/tex]

Hence, the correct answer is:
[tex]\[ \boxed{m} \][/tex]
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