Triangle PQR is dilated by a scale factor of 3 with a center of dilation at the origin. The resulting image is triangle is PQR

1 answer

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.