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Geometric Figures

Geometric Figures. Monday, March 3 rd. Review. 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. Review.

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Geometric Figures

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  1. Geometric Figures Monday, March 3rd

  2. Review 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

  3. Review 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

  4. Review: 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!

  5. Investigative activity #4 • Draw any triangle on the graph paper. • Calculate the midpoint on one of the three sides of your triangle. • Draw lines from these midpoints to the opposite corner of the triangle. These lines are called “medians”. • Repeat steps 2 – 3 for the other two sides. • What do you notice about these three lines?

  6. 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.

  7. Distance between a line and a point What is the fastest way to get to the 401 from point A? 401 hwy Point (x, y)

  8. Distance between a line and a point What is the fastest way to get to the 401 from point A? 401 hwy Path C Path B Path A Point (x, y)

  9. Distance between a line and a point What is the fastest way to get to the 401 from point A? 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

  10. How to calculate the distance between a point and a line • Draw a picture. • Figure out the slope of your original line. • Figure out the slope of your direction line. This is the line that is perpendicular to your original line. • You now have y = mperpx + b for your direction line, but you don’t know b. Figure out b by substituting your point into the line equation. • Determine where the two lines cross by solving a system of two equations (the two lines) and two unknowns (the x, y coordinates of the point where your direction line crosses the original line. • Use your distance formula to find the distance from this crossing location and the original point.

  11. Example If the 401 follows the line: x + y – 5 = 0, and you are parked (in a vehicle that can go over any terrain) at the point (-1, 3), what is the shortest distance to the 401? • Draw a picture. • Figure out the slope of your original line. • Figure out the slope of your direction line. This is the line that is perpendicular to your original line. • You now have y = mperpx + b for your direction line, but you don’t know b. Figure out b by substituting your point into the line equation. • Determine where the two lines cross by solving a system of two equations (the two lines) and two unknowns (the x, y coordinates of the point where your direction line crosses the original line. • Use your distance formula to find the distance from this crossing location and the original point.

  12. Homework • Two Khan Academy check points • Page 95 #1, 2, 5, 21

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