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, 102 + 82 = D2, wecalculate the distance between the two points.100+64 = 164 = D2 . 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.

(x1,y1)

(x2,y2)

To find a formula for this problem, we will create the problem using variables.

(x1,y1)

(x2,y2)

(x2,y1)

x1x2

x2 - x1

D

To find a formula for this problem, we will create the problem using variables.

(x1,y1)

(x2,y2)

(x2,y1)

x1x2

y1

y2

x2 - x1

y2 - y1

D2 = (x2 - x1)2 + (y2 - y1)2

D

D = (x2 - x1)2 + (y2 - y1)2

The distance formula is:

Find the distance between (-2,8) and (9, -5)

D = (9 - (-2))2 + (-5 - 8)2

D = (x2 - x1)2 + (y2 - y1)2

The distance formula is:

Find the distance between (-2,8) and (9, -5)

D = (9 - (-2))2 + (-5 - 8)2

D = 112 + (-13)2

D = (x2 - x1)2 + (y2 - y1)2

The distance formula is:

Find the distance between (-2,8) and (9, -5)

D = (9 - (-2))2 + (-5 - 8)2

D = 112 + (-13)2

D = 121 + 169

D = (x2 - x1)2 + (y2 - y1)2

The distance formula is:

Find the distance between (-2,8) and (9, -5)

D = (9 - (-2))2 + (-5 - 8)2

D = 112 + (-13)2

D = 121 + 169

D = 290