Final answer:
To determine the new location of point D after a translation and reflection over the y-axis, translate D by adding the displacement vector, then reflect it across the y-axis by inverting the x-coordinate.
Step-by-step explanation:
The student asked about the new coordinates of a point D after a translation along a specified vector followed by a reflection over the y-axis. To find the coordinates of the translated point D', we need to add the vector components of the displacement vector to the original coordinates of point D.
Reflection over the y-axis inverts the x-coordinate while keeping the y-coordinate the same. If point D is initially at (-6, 2) and we have a displacement vector with components Dx and Dy, the new point, before reflection, would be D'(-6 + Dx, 2 + Dy). After reflecting over the y-axis, the x-coordinate changes sign, resulting in D''(6 + Dx, 2 + Dy).
Without the exact displacement vector values, we cannot compute the final coordinates. However, the process is to first translate then reflect point D across the y-axis.