distance formula
TRANSCRIPT
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THE DISTANCE FORMULA
During this lesson, we will use the Distance Formula to measure distances on the coordinate plane.
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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.
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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!
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EXAMPLE: Finding the length of a segment, given its endpoints
(X1 –X2)2 + (Y1-Y2)
2
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Let’s Practice:
What is the distance between the points (5, 6) and (– 12, 40) ?
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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
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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
9
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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=