To determine whether the transformation of quadrilateral EFGH is a dilation, we need to check if all points of the original quadrilateral were multiplied by the same scale factor.
First, let's identify the original coordinates of quadrilateral EFGH (though they are not provided in your message, I'll assume you can fill it in based on the context) and the new coordinates after transformation (which you have mentioned).
-
Calculate the scale factor: The scale factor \( k \) can be calculated by selecting a point from the original coordinates and comparing it to its corresponding point in the transformed coordinates. For any point \( (x, y) \), the transformed point will be \( (kx, ky) \).
-
Check consistency: If all points are transformed consistently by the same scale factor, then it is a dilation. If even one point does not follow that rule, it is not a dilation.
Let's evaluate the choices given:
- A. No, because point G'(18 , 42) is incorrect.
- B. Yes, because all points were multiplied by a scale factor of 6.
- C. Yes, because all points were multiplied by a scale factor of 3.
- D. No, because point H'(12 , 27) is incorrect.
Without specific coordinates, you can verify if point G' and point H' are indeed correct based on the calculations outlined above. If they are found to be incorrect according to the scale factor, then options A and D would be valid. If the points match and were consistent with a scale factor of 3 or 6, then options B or C would be valid based on the corresponding scale factor.
Based on that framework, identify the correct option based on your specific coordinates.