A triangle has vertices with coordinates (2, 0), (3, -1), and (-2, -5). If the triangle is dilated by a scale factor of 3 with the origin as the center of dilation, what are the coordinates of the vertices of the image.
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To solve this problem, we need to find the new coordinates of each vertex after the dilation.
Let's start by finding the coordinates of the center of the dilation, which is the origin (0, 0).
Next, we'll find the new coordinates of each vertex by multiplying the original coordinates by the scale factor, which is 3 in this case.
For the first vertex (2, 0), we can multiply each coordinate by 3 to get the new coordinates: (2 * 3, 0 * 3) = (6, 0).
For the second vertex (3, -1), the new coordinates would be: (3 * 3, -1 * 3) = (9, -3).
Similarly, for the third vertex (-2, -5), the new coordinates would be: (-2 * 3, -5 * 3) = (-6, -15).
Therefore, the coordinates of the vertices of the dilated triangle are (6, 0), (9, -3), and (-6, -15).