In the formula d is equal to square root of open paren x sub 2 minus x sub 1 close paren squared plus open paren y sub 2 minus y sub 1 close paren squared end root , how does each subtraction expression relate to the Pythagorean theorem?
Answer
A
Each subtraction expression represents half the length of the hypotenuse of a right triangle with a hypotenuse of length d .
B
Each subtraction expression represents the length of one leg of a right triangle with a hypotenuse of length d .
C
Each subtraction expression represents the square of the length of the hypotenuse of a right triangle with a hypotenuse of length d .
D
Each subtraction expression represents the length of the hypotenuse of a right triangle with a leg of length d .
Explanation
The distance formula is the Pythagorean theorem applied to the horizontal and vertical changes between two points: d² = (x₂ − x₁)² + (y₂ − y₁)². Thus, each subtraction expression gives the length of one leg of a right triangle, and d is the hypotenuse. The correct choice is B, “Each subtraction expression represents the length of one leg.”
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