With respect to the scale factor n, what can be concluded about the ratio of the length of a line segment in an image to its corresponding length in the preimage following a dilation? Explain. How is the slope of a line segment in the image affected by this ratio, if at all? Explain.
Answers
Answer:
What happens if we dilate an entire line?
If that line passes through the point which is the center of the dilation, nothing will change.
Remember that the image point formed by a dilation will lie on a straight line connecting the pre-image point to the center of the dilation. dilate1
The diagram above shows ABline with a center of dilation, labeled O, located on the line. If we choose point B as our pre-image point, we know that its image after the dilation will lie on the line through O and B, which is, of course, Edline. Since O is located on Edline, the image of any point on Edline will lie on Edline.
Conclusion: The dilation of the line, with the center of dilation on the line, leaves the line unchanged (we get the same line again). The scale factor is of no importance.
Keep in mind that this same concept will apply to "segments" in figures.
bullet When the segment (side) of a figure passes through the center of dilation, the segment (side) of the pre-image and its image will be on the same line.
In the diagram at the right, with the center of dilation at (0,-2) and scale factor of 2, we notice that AB dil passes through the center of dilation, (0,-2), which means that AB did and A'B'dil will be on the same line, Edline.
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Answer:
The ratios of the lengths of the line segments in the image to their corresponding lengths in the preimage are equal to the scale factor, n, of the dilation. The slope of the line segments from preimage to image is unchanged by this ratio.
Step-by-step explanation:
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