When triangle PQR is dilated by a scale factor of 3 with a center of dilation at the origin, each vertex of the triangle will be moved away from the origin by a factor of 3.
To determine the new coordinates of the vertices of triangle PQR after the dilation, you can apply the following transformation to each vertex:
If the coordinates of vertex P are \((x_1, y_1)\), vertex Q is \((x_2, y_2)\), and vertex R is \((x_3, y_3)\), the coordinates of the dilated vertices \(P'\), \(Q'\), and \(R'\) will be:
- \(P' = (3x_1, 3y_1)\)
- \(Q' = (3x_2, 3y_2)\)
- \(R' = (3x_3, 3y_3)\)
Thus, the resulting triangle \(P'Q'R'\) will have vertices that are three times farther from the origin than the original triangle \(PQR\). If you provide the specific coordinates of triangle PQR, I can calculate the coordinates of triangle \(P'Q'R'\) for you.