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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 (x1, y1) and (x2, y2), the distance between these points is given by the formula: (X 2 + (Y -Y )2 –X ) 1 2 1 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. A L E R T ! (X1 –X2)2 + (Y1-Y2)2 EXAMPLE: Finding the length of a segment, given its endpoints (X 2 + (Y -Y )2 –X ) 1 2 1 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) B (4,3) AB = ___ A (-1,1) C (3,2) AC = ___ A (-1,1) D (2,-1) AD = __ AB = 13; AC = 17; AD = 13 Now, it’s your turn….. What is the distance between (–2, 7) and (4, 6)? 6.08 What is your answer? _________ What is the distance between (–1, 1) and (4, 3)? 13 What is your answer? _________ ALGEBRA CHALLENGE: If the distance from (x, 3) to (4, 7) is 41 , what is the value of x? 9 What is your answer? _________ 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=