To find the coordinates of point A' after dilating point A(3, -4) by a scale factor of 2 with the center of dilation at the origin, we can use the formula for dilation.
The formula for dilating a point (x, y) from the origin by a scale factor k is:
\[ (x', y') = (k \cdot x, k \cdot y) \]
In this case, the scale factor k is 2, and the coordinates of point A are (3, -4).
Calculating the new coordinates:
\[ x' = 2 \cdot 3 = 6 \] \[ y' = 2 \cdot (-4) = -8 \]
Thus, the coordinates of point A' after dilation are (6, -8).
The correct answer is:
d. (6, -8)