Final answer:
The question is about applying a dilation transformation to points H(1, 2) and G(2, -1) with a center (-1, -1) and a scale factor of 1.5. The new positions are determined by calculating the relative distances from the center, scaling by 1.5, and adding the results back to the center point to obtain H(2, 3.5) and G(3.5, -1).
Step-by-step explanation:
The student has asked about performing a dilation transformation with a scale factor of 1.5 using the center point (-1, -1) on points H(1, 2) and G(2, -1). To do this, we calculate the distance each point is from the center of dilation and multiply each coordinate by the scale factor.
Step-by-Step Dilation of Point H(1, 2)
Calculate the change in x and y from the center of the dilation to point H: (1 - (-1), 2 - (-1)) = (2, 3).
Multiply each coordinate change by the scale factor 1.5: (2 * 1.5, 3 * 1.5) = (3, 4.5).
Add these changes to the center of the dilation to get the coordinates of the dilated point H: (-1 + 3, -1 + 4.5) = (2, 3.5).
Step-by-Step Dilation of Point G(2, -1)
Calculate the change in x and y from the center of the dilation to point G: (2 - (-1), -1 - (-1)) = (3, 0).
Multiply each coordinate change by the scale factor 1.5: (3 * 1.5, 0 * 1.5) = (4.5, 0).
Add these changes to the center of the dilation to get the coordinates of the dilated point G: (-1 + 4.5, -1 + 0) = (3.5, -1).