How do you rotate this for it to look the same and it has no choice but to be rotated.

d

Step-by-step explanation:

The missing options are:

a) line segment EG ≅ line segment E'G'

b) the slope of line segment EF is the same as the slope of line segment E'H'

c) line segment H'F' will overlap line segment HF

d) line segment EH and line segment E'H' both pass through the center of dilation​

The missing picture is shown in the figure attached.

Dilation by a scale factor of 2 means that distance from each new point to point (0,2) is doubled (in each coordinate) than distance from each original point to point (0,2)

For point E(0,5), the distance in x-axis from (0,2) is 0; in y-axis is 5-2 = 3; then E' is located at 2*3 = 6 units above (0,2), that is at (0, 8).

Similarly, point H' is located at (0,0)

F is 1 unit far from (0, 2) in both axis, then F' is 2 units far from (0,2), at (2,0)

G is 2 units far from (0, 2) in x-axis direction, then G' is 4 units far from (0,2)

G is 1 unit far from (0, 2) in y-axis direction, then G' is 2 units far from (0,2)

Location of points are:

E'(0,8)

G'(-4,0)

H'(0,0)

F'(2,0)