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Distance Formula and Midpoint Formula

Distance Formula and Midpoint Formula. Distance Formula. The distance formula is derived from the Pythagorean theorem c 2 = a 2 + b 2 . Substituting d for c, for a, a nd for b in the Pythagorean equation, you get. d.

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Distance Formula and Midpoint Formula

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  1. Distance Formulaand Midpoint Formula

  2. Distance Formula The distance formula is derived from the Pythagorean theorem c2 = a2 + b2. Substituting d for c, for a, and for b in the Pythagorean equation, you get d Parentheses can replace the absolute value symbols since we are squaring. Taking the principal square root yields the distance formula.

  3. The distancedbetween any two points • (x1, y1) and (x2, y2) is given by • Example: Find the distance between the points (6, -1) and (9, 5). Click here to check your answer.

  4. The Midpoint Formula If the endpoints of a segment are and , then the coordinates of the midpoint are .

  5. Midpoint Formula • If the endpoints of a segment are (x1, y1) and (x2, y2), then the coordinates of the midpoint are • Example: Find the midpoint of a segment whose endpoints are (5, 6) and (4, 4). Click here to check your answer.

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