THE DISTANCE FORMULA

During this lesson, we will use the Distance Formula to measure distances on the coordinate plane.

DISTANCE FORMULA

THE DISTANCE FORMULAGiven the two points (x1, y1) and (x2, y2), the distance between these points is given by the formula:

(X1 –X2)2 + (Y1-Y2)

2

Recall: You pick which point is

first, then second.

The diagram below shows the relationship between the Distance Formula and the coordinates of two endpoints of a line segment.

(X1 –X2)2 + (Y1-Y2)2

ALERT!

EXAMPLE: Finding the length of a segment, given its endpoints

(X1 –X2)2 + (Y1-Y2)

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Let’s Practice:

What is the distance between the points (5, 6) and (– 12, 40) ?

Let’s Practice: Find the lengths of the segments. Tell whether any of the segments have the same length. Use the Distance Formula.

A (-1,1)C (3,2)AC = ___

A (-1,1)D (2,-1)AD = __

A (-1,1)B (4,3)AB = ___

AB = 13; AC = 17; AD = 13

Now, it’s your turn…..

What is the distance between (–2, 7) and (4, 6)?

What is your answer? _________

What is the distance between (–1, 1) and (4, 3)?

What is your answer? _________

ALGEBRA CHALLENGE: If the distance from (x, 3) to (4, 7) is 41 , what is the value of x?

What is your answer? _________

6.08

13

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Final Checks for Understanding1. Find the distance between the two points.

C (0,0)

D (5,2)

2. Use the Distance Formula to determine if JK = KL.

J(3,-5); K(-1,2) ; L (-5,-5)

_________________________________

J (3,-5)

K (1,2)

JK=

K (1,2)

L (-5,-5)

KL=