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Wayward wednesday

Wayward wednesday. How can we bend light? . Review day: An overview of the topics you need to know. Wednesday, March 5 th. Recall: Pythagorean Theorem . A 2 + B 2 = C 2. C. A. B. Recall : Delta. Δ means “change in” Δy means “change in y” or “rise” or “y 2 – y 1 ”

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Wayward wednesday

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  1. Wayward wednesday • How can we bend light?

  2. Review day:An overview of the topics you need to know Wednesday, March 5th

  3. Recall: Pythagorean Theorem A2 + B2 = C2 C A B

  4. Recall: Delta Δ means “change in” Δy means “change in y” or “rise” or “y2 – y1” Δx means “change in x” or “run” or “x2– x1”

  5. Length ofLine Segments Pythagorean Theorem: L2= Δy2+ Δx2 L

  6. Equation of a Circle If we fix one end of our line segment to the origin, we can trace out a circle: R2= Δy2+ Δx2 R

  7. 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)

  8. Midpoint formula

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

  10. Parallel and Perpendicular Slopes 1 m mperp = – Perpendicular slope:

  11. Parallel and Perpendicular Slopes 1 m mperp = – Perpendicular slope:

  12. Parallel and Perpendicular Slopes 1 m mperp = – Parallel slope: mparallel= m Perpendicular slope:

  13. Parallel and Perpendicular Slopes 1 m mperp = – Parallel slope: mparallel= m Perpendicular slope:

  14. Geometric shapes B A C The line between these midpoints is parallel to BC The length of the line between these midpoints is half the length of BC

  15. Geometric shapes The perpendicular bisector of any chord in a circle (that’s the line that runs perpendicular to and through the midpoint of a chord) also goes through the center of the circle. chord perpendicular bisector

  16. The circumcenter The circumcenter is the point where the perpendicular bisectors coming from each of the three sides of a triangle intersect. Awesomely enough, it’s also the center of a circle drawn around the triangle!

  17. The Centroid The lines joining the midpoints of each side to the opposite corner are called medians. The centroid is the intersection of the medians of a triangle.

  18. Distance between a line and a point 401 hwy Path B Point (x, y) The shortest distance between a point and a line is a to follow a path that is perpendicular to the line

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