A: The coordinates of the point R' are (- 6, 21).
B: The coordinates of the point T' are (1, 3).
<h3>How to generate new points by definition of dilation</h3>
In this question we must make use of <em>rigid</em> transformations to find the location of new points, <em>rigid</em> transformations are transformations used in <em>geometric</em> loci such that <em>Euclidean</em> distance is conserved. In this case, we need to use a kind of <em>rigid</em> transformation known as dilation, which is defined below:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)] (1)
Where:
- O(x, y) - Center of dilation
- k - Dilation factor
- P(x, y) - Original point
- P'(x, y) - Resulting point
Part A - If we know that O(x, y) = (0, 0), R(x, y) = (- 2, 7) and k = 3, then the coordinates of point R' are:
R'(x, y) = (0, 0) + 3 · [(- 2, 7) - (0, 0)]
R'(x, y) = (- 6, 21)
Part B - If we know that O(x, y) = (- 2, 7), T(x, y) = (4, - 1) and k = 1/2, then the coordinates of point T' are:
T'(x, y) = (- 2, 7) + (1 / 2) · [(4, - 1) - (- 2, 7)]
T'(x, y) = (- 2, 7) + (1 / 2) · (6, - 8)
T'(x, y) = (- 2, 7) + (3, - 4)
T'(x, y) = (1, 3)
To learn more on dilations: brainly.com/question/13176891
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