Distance and Mid point. Quick review: The coordinate plane 4 Quadrants X axis, horizontal Y axis,...
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Transcript of Distance and Mid point. Quick review: The coordinate plane 4 Quadrants X axis, horizontal Y axis,...
Quick review: The coordinate plane
• 4 Quadrants
• X axis, horizontal
• Y axis, vertical
• Plotting point (3, -2)
start at origin (0,0)
x, go left (-) or right (+)
y, go up(+) or down(-)
I
III
II
IV(3, -2)
Line Segment vs Line• Iines go on forever,
arrows on each end
• Line segments have end points
• The length of a line segment is the distance between the two endpoints
• Often the end points are assigned letters
(4,3)
(-4,-4)A
B
Length of a Line Segment• What is the length of
this line segment?
Count the spaces from one end point to the other
(4,3)
(4,-4)
A
B
7 units
Length of a Line Segment• What about the length
of this one?
Count the spaces from one end point to the other
(-2,-3)
(4,-4)AB
6 units
Length of a Line Segment• When the line segment
is like this, it is not so easy to find the exact length.
• Just for kicks, estimate how long you think it is
• About 8? 9?
• To find this exact length we use the distance formula
(4,3)
(-4,-4)A
B
Example
• Find the distance between A(-4,-4) and B(4,3)
2 2distance ( ) ( )x x y y
A (-4, -4) B (4, 3)
2 2distance (4 ( 4)) (3 ( 4))
2 2distance (8) (7)
distance 64 49 113 10.63014581
Example
• Find the distance between A(-4,-4) and B(4,3)
2 2distance ( ) ( )x x y y
A (-4, -4) B (4, 3)
2 2distance (4 ( 4)) (3 ( 4))
2 2distance (8) (7)
distance 64 49 113 10.63
YOU TRY!!
• Find the distance between:– A. (2, 7) and (11, 9)
– B. (-5, 8) and (2, - 4)
2 2(9) (2) 85
2 2(7) ( 12) 193
Distance Vs Midpoint• Distance is the
length between two points
• Midpoint is the point that is exactly half way between two points.
9.21 units
(.5,0)
Example
• Find the midpoint between A(4,8) and B(1,12)
midpoint ,2 2
x x y y
A (4, 8)
B (1, 12)
1 4 12 8midpoint ,
2 2
midpoint 5,10
2 2.5,10or
SAD STACKERA way to remember the midpoint formula
•Stack em
•Add em
•Divide by 2
(4 , 8 )
(1, 12)
(5, 20)
2 2
(2.5, 10)
• Find the midpoint between A(4,8) and B(1,12)