Final answer:
Option B provides a set of points that represent a dilation of triangle RST from the origin with a consistent scale factor of 6 applied to the x-coordinates, while the y-coordinates remain unchanged. Thus, R’ (0, 2), S' (18,8), T’ (36,2) is the correct dilation.
Step-by-step explanation:
To determine which set of points represents a dilation of the triangle RST from the origin, we look for a constant scale factor applied to the coordinates of R (0,2), S (3,8), and T (6,2). A dilation from the origin means that each coordinate of R', S', and T' should be the original coordinate of R, S, and T respectively, multiplied by the same scale factor.
By checking the given options, we see that only option B satisfies this condition:
- R’ (0, 2) is 0 and 2 multiplied by 1, retaining the original R.
- S' (18,8) means 3 multiplied by 6 and 8 multiplied by 1, not respecting the same factor for both x and y.
- T’ (36,2) has 6 multiplied by 6 for the x-coordinate, and 2 remains the same, indicating the scale factor for the x-coordinate is 6 and for the y-coordinate is 1.
Since B is the only option where the x-coordinates have been consistently multiplied by the same factor (6), and the y-coordinates have remained unchanged (indicating a scale factor of 1), B is the correct answer.