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

DISTANCE FORMULA THE DISTANCE FORMULA Given the two points (x 1, y 1 ) and (x 2, y 2 ), the distance between these points is given by the formula:  (X 1 –X 2 ) 2 + (Y 1 -Y 2 ) 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.Distance Formula  (X 1 –X 2 ) 2 + (Y 1 -Y 2 ) 2 ALERT!ALERT!

EXAMPLE: Finding the length of a segment, given its endpoints  (X 1 –X 2 ) 2 + (Y 1 -Y 2 ) 2

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? _________ Check your answers HERE  13 9

Final Checks for Understanding 1.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=