The center of dilation (1,4) is found in one of the vertex of this triangle; This point and its image are the same.
Now, we have to get two sides with twice distance, because the dilation factor is 2, because the center of dilation is found in the right vertex also the triangle must have the same shape.
Other vertex is (4,4) because the scale factor is 2, this side between the vertex [(1,4) to (4,4)]will have the twice distance; Distance: 3, then the new vertex will be (4+3, 4)=(7,4)
Other vertex is (1,6) because the scale factor is 2; The side between the vertex (1,4) up (1,6) will have the twice distance; Distance:2; then the new vertex will be (1,6+2)=(1,8).
Answer; the news coordinates would be: (1,4), (7,4) and (1,8).