Answer: The image of the triangle after the dilation with a scale factor of 1/3 centered at the origin is A'(0, 1), B'(2, 0), and C'(0, -1).
Explanation:
To find the coordinates of the triangle's image after a dilation with a scale factor of 1/3 centered at the origin, you can multiply the x and y coordinates of each vertex by the scale factor.
Let's calculate the new coordinates for each vertex:
A(0, 3):
New x-coordinate: 0 * (1/3) = 0
New y-coordinate: 3 * (1/3) = 1
So, the new coordinates for A are (0, 1).
B(6, 0):
New x-coordinate: 6 * (1/3) = 2
New y-coordinate: 0 * (1/3) = 0
So, the new coordinates for B are (2, 0).
C(0, -3):
New x-coordinate: 0 * (1/3) = 0
New y-coordinate: -3 * (1/3) = -1
So, the new coordinates for C are (0, -1).
The image of the triangle after the dilation with a scale factor of 1/3 centered at the origin is A'(0, 1), B'(2, 0), and C'(0, -1).