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This problem trains for: SAT-I, AMC-8, GMAT.

If the Queen of Hearts is at coordinates (-2, -7), Alice is at coordinates (3, 5) and the Knave of Hearts is at (4.5, -4) what is the distance from the Knave to the hedgehog which is exactly midway between the Queen and Alice?

(characters from Lewis Carroll's "Alice in Wonderland")

The midpoint formula gives us the coordinates of the hedgehog:

equation

and the distance formula gives us the distance between the Knave and the hedgehog:

equation

equation