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Distance, Midpoint, Pythagorean Theorem

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Distance, Midpoint, Pythagorean Theorem
Distance, Midpoint,
Pythagorean Theorem
Distance Formula
• Distance formula—used to measure the
distance between between two endpoints of
a line segment (on a graph).
d  ( x1  x2 )  ( y1  y2 )
2
2
• x1 and y1 are the coordinates of the first point
• x2 and y2 are the coordinates of the second point
Distance Formula
• Find the distance between the points (1, 2)
and (–2, –2).
• Your video game uses a coordinate grid
system for location. There is an enemy ship
at (7, –3). You are at (–8, –3). If one grid
unit equals 10 miles, how far away is the
enemy ship?
Midpoint Formula
• Midpoint formula—used to find the
midpoint of a line segment. (It will always
be in the form of a point (x, y).)
 x1  x2 y1  y2 
M 
,

2 
 2
• x1 and x2 are the x-coordinates of the points
• y1 and y2 are the y-coordinates of the points
Midpoint Formula
• Find the midpoint of the segment given the
endpoints (5, 7) and (13, 1).
• What is the midpoint of the line segment
with endpoints (–3, –3) and (7, 3)?
• Line segment CD has a midpoint at (1, 2). If
endpoint C is located at (–5, 3), find the
ordered pair represented the other endpoint D.
Pythagorean Theorem
• Pythagorean Theorem—In a right
triangle, the sum of the squares of the two
legs equals the hypotenuse squared.
• a 2 + b2 = c 2
a and b are legs
c is the hypotenuse
Pythagorean Theorem
hypotenuse
leg
leg
The hypotenuse is always the longest side of a right
triangle and is always opposite the right angle.
Pythagorean Theorem
• What is the value of the missing side?
5
12
Pythagorean Theorem
• What is the value of the missing side?
9
15
Pythagorean Theorem
• The perimeter of a square is 36 inches.
What is the length of its diagonal?
Homework
• Pg. 552 (#10, 11, 14, 15, 22-27)
• Pg. 557 (#10-18 find distance AND midpoint)
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