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Published byRobert McCoy Modified over 8 years ago

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The Distance Formula

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The distance formula is used to find the Length of the segment

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Let’s look at the segment without the grid Now let’s label the endpoints, using a general notations for a grid.

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Form a right triangle

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Using Pythagorean Theorem let’s find the distance formula Pythagorean Theorem Set up to solve for our segment, c Use the Symmetric Property

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Define the Variables Of Pythagorean Theorem Let a be the altitude, y Let b be the base, x and Let c be the distance, d

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Substitution becomes

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Take the Square Root both sides What do you get?

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Let’s Try it with numbers! Let (x 1,y 1 ) and (x 2,y 2 ) be (2,3) and (5,8) Substitute into the distance formula

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Substituted Simplified, order of operation

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When do we use this? Distance formula is used to find a length of a segment on a Cartesian Plane. We will use this in conjunction with slope to prove or to disprove a quadrilateral is a square, rectangle, parallelogram or a rhombus. We may also use it to prove or disprove that a triangle is equilateral or isosceles. The End

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