Final answer:
The x-coordinate of D' after reflection over the y-axis is 3.
Step-by-step explanation:
When reflecting a point over the y-axis, the x-coordinate changes sign while the y-coordinate remains constant. This geometric transformation occurs by flipping the position of the point across the y-axis.
Given the point D(-3, 1), reflecting it over the y-axis involves changing the sign of its x-coordinate while keeping the y-coordinate unchanged. The reflection formula for a point (x, y) over the y-axis is (-x, y).
For point D(-3, 1), reflecting it over the y-axis yields a new point, let's call it D'. The x-coordinate of D' will be the negative of the original x-coordinate of D, while the y-coordinate remains the same. So, applying the reflection formula:
Original x-coordinate of D = -3. When reflected over the y-axis, the x-coordinate changes sign: -(-3) = 3.
Therefore, after reflecting point D(-3, 1) over the y-axis, the x-coordinate of the new point D' becomes 3. This transformation positions the reflected point D' at (3, 1), indicating that it is equidistant from the y-axis but on the opposite side compared to the original point D.