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Advanced Topic for 9 th & 10 th only

Learn about finding the distance between a point and a line by drawing perpendiculars and identifying equidistant lines. Understand the concept of equidistant lines and the theorem stating that equidistant lines from a third line are parallel. Practice solving problems involving parallel lines and finding distances using the distance formula.

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Advanced Topic for 9 th & 10 th only

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  1. Advanced Topic for 9th & 10th only

  2. Chapter 3-6Perpendiculars and Distance

  3. B A Distance between a Point and a Line: The distance between a point and a line, is the length of the segment perpendicular to the line from the point. Shortest distance C

  4. Which segment in the diagram represents the distance from Rto XY? • A • B • C • D ___ ___ ___ ___ RY RX MX RM

  5. d d a b c Equidistant: same distance. Theorem: In a plane if two lines are equidistant from a third line, then the two lines are parallel to each other. If the distance between line a and b is d and distance between b and c is d then a and c are Parallel.

  6. Find the distance between the parallel lines

  7. Graph the original two equations.

  8. Use to find the equation of the line perpendicular to the original two equations. Use one of the y intercepts of the original equations. So the equation of the green line is

  9. Use system of equations to determine where the green line intersects the top blue equation. =

  10. Now you know that at x=1 the green graph crosses the graph on top, plug in x=1 into the equation of the green line. The intersection point is (1,0)

  11. Now use the distance formula: Between points (0,-3) and (1,0).

  12. Homework • Textbook pages 185 – 187, • problems 1, 4 – 7, 10 – 18 evens, • and 36 – 42 evens.

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