Question
If you dilate triangle XYZ to form X'Y'Z' using a magnitude (scale factor) of 3 and a center dilation at the origin, what are the coordinates of the dilated triangle? (1 point) Responses X' (6, 12), Y' (6,18), Z' (21,6) X' (6, 12), Y' (6,18), Z' (21,6) X' (-3,6), Y' (6,0), Z' (7, 2) X' (-3,6), Y' (6,0), Z' (7, 2) X' (-3,6), Y' (6, 18), Z' (27, 6) X' (-3,6), Y' (6, 18), Z' (27, 6) X' (-1,2), Y' (6, 15), Z' (27,6)
Answers
GPT-4o mini
To find the coordinates of the dilated triangle X'Y'Z' given a scale factor of 3 and a center of dilation at the origin (0, 0), you multiply each coordinate of the original triangle by 3.
Let's denote the original coordinates of the triangle as follows:
- X(x1, y1)
- Y(x2, y2)
- Z(x3, y3)
The coordinates after dilation will be:
- X' = (3 * x1, 3 * y1)
- Y' = (3 * x2, 3 * y2)
- Z' = (3 * x3, 3 * y3)
However, since the original coordinates are not provided in your question, it is impossible to directly compute the coordinates of the new triangle. If you can provide the original coordinates of triangle XYZ, I can calculate the coordinates of the dilated triangle X'Y'Z' for you.
Based on the given options, the dilation will make all coordinates scale accordingly based on your original points. Please supply those original coordinates to proceed or clarify.
Let's denote the original coordinates of the triangle as follows:
- X(x1, y1)
- Y(x2, y2)
- Z(x3, y3)
The coordinates after dilation will be:
- X' = (3 * x1, 3 * y1)
- Y' = (3 * x2, 3 * y2)
- Z' = (3 * x3, 3 * y3)
However, since the original coordinates are not provided in your question, it is impossible to directly compute the coordinates of the new triangle. If you can provide the original coordinates of triangle XYZ, I can calculate the coordinates of the dilated triangle X'Y'Z' for you.
Based on the given options, the dilation will make all coordinates scale accordingly based on your original points. Please supply those original coordinates to proceed or clarify.