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The Distance Formula

The Distance Formula. The distance formula is used to find the Length of the segment. Now let’s label the endpoints, using a general notations for a grid . Let’s look at the segment without the grid. Form a right triangle. Pythagorean Theorem Set up to solve for our segment, c

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The Distance Formula

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  1. The Distance Formula

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

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

  4. Form a right triangle

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

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

  7. Substitution becomes

  8. Take the Square Root both sides What do you get?

  9. Let’s Try it with numbers! Let (x1,y1) and (x2,y2) be (2,3) and (5,8) Substitute into the distance formula

  10. Substituted Simplified, order of operation The Work

  11. 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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