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Published byElizabeth Brewer Modified over 2 years ago

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The Distance Formula Amy Hatfield Central High School A(-4, 3) B(8, -5)

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Finding the length of vertical or horizontal segments in the coordinate plane is simple: just count the number of blocks from one endpoint to the other! A AB = 8 units B X Y XY = 7 units

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What do you do if the segment isnt horizontal or vertical? You cant count blocks! ?? C(-2, -1) D(3, 2)

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Lets use our geoboards to model this situation. We can form a right triangle with the segment CD as the hypotenuse. C D

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Lets use the Pythagorean Theorem to find the length of segment CD. C D 3 units 5 units a 2 + b 2 = c = c = c 2 c 2 = 34 c = units

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C(x 1, y 1 ) D(x 2, y 2 ) The number 5 came from the positive difference between the two x coordinates, x 1 and x 2. Likewise, the number 3 came from the positive difference between the two y-coordinates, y 1 and y 2.

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Now, using the Pythagorean Theorem, plug in the variables instead of the numbers. c 2 = a 2 + b 2 d 2 = (x 2 – x 1 ) 2 + (y 2 - y 1 ) 2 d = (x 2 – x 1 ) 2 + (y 2 - y 1 ) 2 This is the distance formula!!

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