The distance between the points (d) is found using the Pythagorean theorem.
Imagine the two points as defining the hypotenuse of a right triangle. The lengths of the legs of the triangle are the horizontal distance between the points and the vertical distance between the points. The the theorem tells us
d² = 4² + 7²
d² = 16 + 49
d² = 65
d = √65 ≈ 8.1
The distance between the points is
C 8.1
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You know that the distance must be longer than the longest leg (7) and must be shorter than the sum of the two legs (4+7=11). The only answer choice between 7 and 11 is 8.1.
