Graph the image of this figure after a dilation with a scale factor of 1/3 centered at the origin

The dilation of a figure with a scale fator k means that the distance of each point of the image from the center of dilation will be k times the distance of the original figure from the center of dilation.
Also the length of each two points of the image is k times the length of each two points of the original figure.

From the given figure, the vertices of the original triangle are (-3, 3), (6, 6) and (3, 9).

The vertices of the image of this figure after a dilation with a scale factor of 1/3 centered at the origin is given by

[tex] \frac{1}{3} (-3, 3),\ \frac{1}{3} (6, 6)\ and\ \frac{1}{3} (3, 9) \\ \\ =(-1,1),\ (2,2)\ and\ (1,3)[/tex]

Therefore, the verties of the image of this figure after a dilation with a scale factor of 1/3 centered at the origin are (-1, 1), (2, 2) and (1, 3).