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Midpoint of a line segment

Midpoint of a line segment. Tuesday Feb 25 . Midpoint of a horizontal line. Midpoint of a horizontal line: . x 1 + x 2 2. y 1 + y 2 2. x m = . y m = . Midpoint formula. Example. Braden skis (or snowboards?) from (3, -9) to (7, -14) down one segment of the hill.

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Midpoint of a line segment

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  1. Midpoint of a line segment Tuesday Feb 25

  2. Midpoint of a horizontal line Midpoint of a horizontal line: x1 + x2 2 y1 + y2 2 xm = ym=

  3. Midpoint formula

  4. Example Braden skis (or snowboards?) from (3, -9) to (7, -14) down one segment of the hill. • What is the distance that Braden travels? • What is the midpoint in this line?

  5. Parallelograms • The diagonals of a parallelogram intersect at their midpoints. This means that they “bisect” each other.

  6. Parallelograms • Find the bisection point of this parallelogram:

  7. Try in your teams 1. In the volleyball game on Friday, Michelle bumps the ball from (2, –3) to Amy at (–5, –11). • What is the distance between Michelle and Amy? • What is the midpoint between Michelle and Amy? 2. Find the bisection point of this parallelogram:

  8. Try in your teams 1. In the volleyball game on Friday, Michelle bumps the ball from (2, –3) to Amy at (–5, –11). • What is the distance between Michelle and Amy? Ans: 13.15m • What is the midpoint between Michelle and Amy? Ans: (-1.5, -7) 2. Ans: (-2, 5)

  9. Practice Individually • Page 77 #1 – 6 Draw the parallelogram (-3, 1), (4, 3), (3, -3), (-4, -5). Determine the midpoints of each line segment in this parallelogram. Calculate the perimeter of the quadrilateral that you can draw between these midpoints.

  10. Equation of a Circle Pythagorean Theorem: L2= Δy2+ Δx2 L

  11. Equation of a Circle Pythagorean Theorem: L2= Δy2+ Δx2 L

  12. Equation of a Circle Pythagorean Theorem: L2= Δy2+ Δx2 L

  13. Equation of a Circle Equation for a circle: R2 = Δx2 + Δy2 R Equation for a circle centered at (0, 0): R2= y2+ x2

  14. Equation for a circle For example, this circle has the equation: x2 + y2 = 25

  15. Equation for a circle What is the equation of this circle? Equation for a circle: R2 = Δx2 + Δy2 R2 = (x – a)2 + (y – b)2 where the center of the circle is (a, b)

  16. Equation for a circle Example: What is the equation for this circle?

  17. Try in your teams • A circle has a center at (-2, 3) and the point (-1, 7) is on the outer edge of the circle. What is the equation for the circle? • Extra challenge: What is the equation of a circle that has a diagonal from (-1, 4) to (3, 11?

  18. Homework Page 71 #1 – 4, 6 Page 78 #9, 12, 16 – 20

  19. Homework Page 71 #1 – 4, 6, 18 Page 78 #9, 12, 16 – 20

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