Amy Hatfield Central High School

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

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

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)

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

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

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)

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!!