Since the two triangles ABC and ADE are similar, their corresponding sides are proportional. We can use this fact to find the coordinates of point E.
Let's first find the coordinates of point D. We know that D lies on the line AB and that AD is 1/2 the length of AB. Therefore, the x-coordinate of D is halfway between the x-coordinates of A and B, and the y-coordinate of D is halfway between the y-coordinates of A and B. Using the coordinates of A and B, we get:
x-coordinate of D = (1 + 4)/2 = 2.5
y-coordinate of D = (-2 + 3)/2 = 0.5
Now, since triangles ABC and ADE are similar, the ratio of the length of side AB to side AD is equal to the ratio of the length of side BC to side DE. We can use this fact to find the length of DE:
AB/AD = BC/DE
5/2 = 3/DE
DE = (2/5) * 3 = 6/5
Finally, we can use the coordinates of D and the length of DE to find the coordinates of E. Since E lies on the line AD, its x-coordinate is the same as that of D. To find its y-coordinate, we need to add the length of DE to the y-coordinate of D. Using the coordinates of D and the length of DE, we get:
x-coordinate of E = 2.5
y-coordinate of E = 0.5 + 6/5 = 2.1
Therefore, the coordinates of point E are (2.5, 2.1).