If the Earth is represented by a basketball placed mid-court, how far away should the object representing the Moon be placed?

The moon should be at 543 cm.

Explanation:

If according to scientists the distance from the earth to the moon is approximately 384400 km

.

The earth has a radius of 6371 km.

A basketball has a radius of 9 cm.  (Using a basketball of this radius as a reference)

With these data you can make a rule of 3:

The earth in centimeters has a radius of 6.371e+8 cm.

So: If the earth has a radius of 6.371e+8 cm and a distance to the moon of 384,400 km, what would the distance be if the earth had a radius of 9 cm?

6.371e+8 cm      :      9 cm

384400 km       :       X

X = (384400 km * 9 cm) / 6.371e+8 cm

X = 5.43e-3 km converting to centimeters would give that:

X = 543 cm

The moon should be at 543 cm from Earth.