Final answer:
Option B, with the coordinates K'(-6, 9), L'(3, 24), M'(12, 9), is the correct set of points representing a dilation from the origin of triangle KLM, as the scale factors are consistent at 3 for both the x and y coordinates.
Step-by-step explanation:
To determine which set of points represents a dilation from the origin of triangle KLM with coordinates K(-2, 3), L(1, 8), and M(4, 3), we need to look at the ratios of the coordinates of the dilated points to the original points. The coordinates must be scaled by the same factor for both the x and y values. Let's consider the choices given:
- A. K'(1, 6), L'(4, 11), M'(7, 6)
- B. K'(-6, 9), L'(3, 24), M'(12, 9)
- C. K'(-6, 3), L'(1, 24), M'(12, 3)
- D. K'(-6, 3), L'(3, 8), M'(12, 3)
By analyzing the scale factors between the original points and the corresponding dilated points, we can see that Option B has consistent scale factors of 3 for both the x and y coordinates (e.g., K' is -2 × 3 = -6 for x and 3 × 3 = 9 for y), which signifies a dilation factor of 3 from the origin. Therefore, Option B is the correct set of points representing a dilation from the origin of triangle KLM.