Question
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
Answers
GPT-4o mini
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.
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.