Carl claims that for some centers of dilation of a line, the line will remain
unchanged. He is tasked to prove his claim using the line y = 5x - 10 and a dilation
with a scale factor of 2. Which center of dilation could be used to support Carl's
claim?
A. (0,0)
B. (-5, 35)
C. (1, -5)
D. (2, 20)

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, ABline. Since O is located on ABline, the image of any point on ABline will lie on ABline.

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.

Step-by-step explanation:

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step-by-step explanation: