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**Amy Hatfield Central High School**

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

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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 B X Y AB = 8 units XY = 7 units

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**What do you do if the segment isn’t horizontal or vertical**

What do you do if the segment isn’t horizontal or vertical? You can’t count blocks! ? ? D(3, 2) C(-2, -1)

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**Let’s use our geoboards to model this situation**

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

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**Let’s use the Pythagorean Theorem to find the length of segment CD.**

3 units C 5 units a2 + b2 = c2 = c2 = c2 c2 = 34 c =34 5.83 units

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**The number 5 came from the positive difference between the two x coordinates, x1 and x2.**

Likewise, the number 3 came from the positive difference between the two y-coordinates, y1 and y2. D(x2, y2) C(x1, y1)

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**This is the distance formula!!**

Now, using the Pythagorean Theorem, plug in the variables instead of the numbers. c2 = a2 + b2 d2 = (x2 – x1)2 + (y2 - y1)2 d = (x2 – x1)2 + (y2 - y1)2 This is the distance formula!!

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Pythagorean Theorem & Distance Formula Anatomy of a right triangle The hypotenuse of a right triangle is the longest side. It is opposite the right angle.

Pythagorean Theorem & Distance Formula Anatomy of a right triangle The hypotenuse of a right triangle is the longest side. It is opposite the right angle.

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