To dilate triangle ABC by a scale factor of 4 with the center at the origin, you multiply each coordinate of the triangle's vertices by the scale factor.
Given point A with coordinates (3, -4), the dilation is calculated as follows:
\[ A' = (x \cdot k, y \cdot k) \] where \(k\) is the scale factor.
For point A (3, -4): \[ A' = (3 \cdot 4, -4 \cdot 4) = (12, -16) \]
So, after dilation, point A will be at (12, -16).
If you are referring to a point with coordinates (6, -8), that is not the dilation of point A. The point resulting from dilating A by a factor of 4 is (12, -16).
If you have other vertex coordinates to dilate, please provide them and I can calculate those as well!