The Distance and Midpoint Formulas Goal 1
Find the Midpoint of a Segment
Goal 2
Find the distance between two points on a coordinate plane
Goal 3
Find the slope of a line between two points on a coordinate plane
Distance Formula
Used to find the distance between two points
( x1 , y1 )and ( x2 , y2 )
distance = ( x2 − x1 ) + ( y2 − y1 ) 2
2
Example
Find the distance between (2,1) and (5,2). x1 y1
D= (2 - 5)² + (1 - 2)² D= (-3)² + (-1)² D= 9+1 D= 10 D= 3.162
x2 y2
-First substitute numbers for variables and solve the parentheses. -Then solve the squared number. -Add the two numbers. -Find the square root of the remaining number.
Example
Find the distance between A(4,8) and B(1,12)
A (4, 8)
B (1, 12)
( x1 , y1 ) and ( x2 , y2 ) distance = ( x2 − x1 ) + ( y2 − y1 ) 2
distance = (1 − 4) + (12 − 8) 2
distance = ( −3) + (4) 2
2
2
distance = 9 + 16 = 25 =
5
2
YOU TRY!!
Find the distance between:
A. (2, 7) and (11, 9)
(9) + (2) = 85 2
2
B. (-5, 8) and (2, - 4)
(7) + (−12) = 193 2
2
Midpoint Formula
Used to find the center of a line segment
( x1 , y1 )and ( x2 , y2 )
x2 + x1 y2 + y1 midpoint = , ÷ 2 2
Example
Find the midpoint between A(4,8) and B(1,12)
A (4, 8)
B (1, 12)
x2 + x1 y2 + y1 midpoint = , ÷ 2 2
1 + 4 12 + 8 midpoint = , ÷ 2 2 midpoint = 5 ,10 ÷ 2
YOU TRY!!
Find the midpoint between:
A)
(2, 7) and (14, 9)
midpoint = ( 8,8 )
B)
(-5, 8) and (2, - 4)
-3 midpoint = , 2 ÷ 2
y2 − y1 m= x2 − x1 THE SLOPE FORMULA!
(6, 5)
x2 y 2
Use the slope formula
y2 − y1 x2 − x1 ( -5, -3)
x1 y1
−3−5 −8 8 = = − 11 11 −5−6
Classwork ď Ž
Complete the handout given in class.
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