[tex]\boxed{A'(4,24) \ and \ B'(8,-16)}[/tex]
When we dilate objects we enlarge or reduce the size of that object. We need to consider the scale factor and the center of dilation. In this exercise, the scale factor is 4. Since this number is greater than 1, then our resulting line segment will be larger than the original. In this problem, we will assume the center of dilation at the origin, so we just need to multiply the x and y coordinates of each point by 4. So:
[tex]A' \rightarrow A'(1\times 4, 6\times 4)=A'(4,24) \\ \\ B' \rightarrow B'(2\times 4, -4\times 4)=B'(8,-16)[/tex]
Finally, the coordinates of the line segment are:
[tex]\boxed{A'(4,24) \ and \ B'(8,-16)}[/tex]
Dilation: https://brainly.com/question/10946046
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