Distance, Midpoint, Pythagorean Theorem

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Distance, Midpoint, Pythagorean Theorem
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Distance Formula

• Distance formulaused to measure the distance
  between between two endpoints of a line segment
  (on a graph).

• x1 and y1 are the coordinates of the first point
• x2 and y2 are the coordinates of the second point

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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?

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Midpoint Formula

• Midpoint formulaused to find the midpoint of a
  line segment. (It will always be in the form of
  a point (x, y).)

• x1 and x2 are the x-coordinates of the points
• y1 and y2 are the y-coordinates of the points

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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.

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Pythagorean Theorem

• Pythagorean TheoremIn 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

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Pythagorean Theorem
hypotenuse
leg
leg
The hypotenuse is always the longest side of a
right triangle and is always opposite the right
angle.
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Pythagorean Theorem

• What is the value of the missing side?

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12
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Pythagorean Theorem

• What is the value of the missing side?

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Pythagorean Theorem

• The perimeter of a square is 36 inches. What is
  the length of its diagonal?

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Homework

• Pg. 552 (10, 11, 14, 15, 22-27)
• Pg. 557 (10-18 find distance AND midpoint)