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Distance, Midpoint, Pythagorean Theorem. Distance Formula. Distance formula —used to measure the distance between between two endpoints of a line segment (on a graph). x 1 and y 1 are the coordinates of the first point x 2 and y 2 are the coordinates of the second point. - PowerPoint PPT Presentation
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Distance Formula• Distance formula—used to measure the
distance between between two endpoints of a line segment (on a graph).
d x x y y ( ) ( )1 22
1 22
• 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).)
2
,2
2121 yyxxM
• 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.
• a2 + b2 = c2
a and b are legs
c is the hypotenuse
Pythagorean Theorem
leg
leg
hypotenuse
The hypotenuse is always the longest side of a right triangle and is always opposite the right angle.