Answer:A' = (15, -15), B' = (9, -9), and C' = (15, -9)
Explanation:
To dilate triangle ABC with a center of dilation at the origin (0,0) and a scale factor of 3, you need to multiply the coordinates of each vertex by the scale factor.
Let's calculate the coordinates of triangle A'B'C':
For point A:
x-coordinate of A' = scale factor * x-coordinate of A = 3 * 5 = 15
y-coordinate of A' = scale factor * y-coordinate of A = 3 * (-5) = -15
Therefore, A' = (15, -15)
For point B:
x-coordinate of B' = scale factor * x-coordinate of B = 3 * 3 = 9
y-coordinate of B' = scale factor * y-coordinate of B = 3 * (-3) = -9
Therefore, B' = (9, -9)
For point C:
x-coordinate of C' = scale factor * x-coordinate of C = 3 * 5 = 15
y-coordinate of C' = scale factor * y-coordinate of C = 3 * (-3) = -9
Therefore, C' = (15, -9)
Hence, the correct coordinates of triangle A'B'C' are A' = (15, -15), B' = (9, -9), and C' = (15, -9).