Solution
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Dilation is the enlargement or reduction in the size of an image. If a point A(x, y) is dilated by a factor k, the new point is A'(kx, ky).
A Dilation is defined as a transformation in which the Image (The figure obtained after the transformation) and the Pre-Image (The original figure, before the transformation) have the same shape, but their sizes are different.
In this case you know that the triangle ABC is dilated by a scale factor of 3 with a center of dilation at the origin.
Given triangle ABC has vertices at A(-1, 0), B(0, 1), C(3, 0).
If the triangle is dilated by a scale factor of 3, the new point is:
The new point is: A'(-1/3, 0), B'(0, 1/3), C'(1, 0). Hence the area of the triangle after dilation will be (one third) of the old points