If we apply a dilation with center P and scale factor 1/3 to triangle ABC, then every point on the triangle will move towards P, and the distance between each point and P will be reduced to one-third of its original value.
The image of triangle ABC under this dilation will be a new triangle A'B'C', where A', B', and C' are the images of A, B, and C, respectively. The new triangle will be smaller than the original triangle, and its vertices will be located closer to P.
To find the image of each vertex, we can draw a line segment from P to each vertex, and then mark the point on each segment that is one-third of the distance from P to the corresponding vertex. The new triangle will be formed by connecting these three new points.
Note that the dilation will preserve the shape of the triangle, so the angles of the new triangle will be congruent to the corresponding angles of the original triangle. However, the sides of the new triangle will be one-third the length of the corresponding sides of the original triangle.