Presentation on theme: "Amy Hatfield Central High School"— Presentation transcript:
1 Amy Hatfield Central High School The Distance FormulaA(-4, 3)B(8, -5)Amy HatfieldCentral High School
2 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!ABXYAB = 8 unitsXY = 7 units
3 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)
4 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.DC
5 Let’s use the Pythagorean Theorem to find the length of segment CD. 3 unitsC5 unitsa2 + b2 = c2= c2= c2c2 = 34c =34 5.83 units
6 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)
7 This is the distance formula!! Now, using the Pythagorean Theorem, plug in the variables instead of the numbers.c2 = a2 + b2d2 = (x2 – x1)2 + (y2 - y1)2d = (x2 – x1)2 + (y2 - y1)2This is the distance formula!!