Finding the distance between two points. (-4,4) (4,-6)

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Presentation transcript:

Finding the distance between two points. (-4,4) (4,-6)

Finding the distance between two points. Draw the right triangle as shown. (-4,4) (4,-6)(-4,-6) 4-(-6)=10

Find the length of each leg. (-4,4) (4,-6) (-4,-6) 10 4-(-4)=8

Using the Pythagorean theorem, = D 2, we calculate the distance between the two points = 164 = D 2. Thus D = 164 (-4,4) (4,-6) (-4,-6) 10 4-(-4)=8

To find a formula for this problem, we will create the problem using variables. (x 1,y 1 ) (x 2,y 2 )

To find a formula for this problem, we will create the problem using variables. (x 1,y 1 ) (x 2,y 2 ) (x 2,y 1 ) x1x1 x2x2 x 2 - x 1 D

To find a formula for this problem, we will create the problem using variables. (x 1,y 1 ) (x 2,y 2 ) (x 2,y 1 ) x1x1 x2x2 y1y1 y2y2 x 2 - x 1 y 2 - y 1 D 2 = (x 2 - x 1 ) 2 + (y 2 - y 1 ) 2 D

D = (x 2 - x 1 ) 2 + (y 2 - y 1 ) 2 The distance formula is: Find the distance between (-2,8) and (9, -5) D = (9 - (-2)) 2 + (-5 - 8) 2

D = (x 2 - x 1 ) 2 + (y 2 - y 1 ) 2 The distance formula is: Find the distance between (-2,8) and (9, -5) D = (9 - (-2)) 2 + (-5 - 8) 2 D = (-13) 2

D = (x 2 - x 1 ) 2 + (y 2 - y 1 ) 2 The distance formula is: Find the distance between (-2,8) and (9, -5) D = (9 - (-2)) 2 + (-5 - 8) 2 D = (-13) 2 D =

D = (x 2 - x 1 ) 2 + (y 2 - y 1 ) 2 The distance formula is: Find the distance between (-2,8) and (9, -5) D = (9 - (-2)) 2 + (-5 - 8) 2 D = (-13) 2 D = D = 290