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Geometry

Geometry. 3.6 Perpendiculars and Distance. The distance between a line and a point not on the line is the length of the segment perpendicular to the line from the point. Postulate 3.6 Perpendicular Postulate.

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Geometry

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  1. Geometry 3.6 Perpendiculars and Distance

  2. The distance between a line and a point not on the line is the length of the segment perpendicular to the line from the point.

  3. Postulate 3.6Perpendicular Postulate • If given a line and a point not on the line, then there exists exactly one line through the point that is perpendicular to the given line.

  4. Ex. 1 • Copy the figure and construct the segment that represents the distance from Q to segment RS. S R Q P

  5. Steps to find distance if given a line and a point • 1) Find the equation for the given line. • 2) Write an equation for line perpendicular to the given line through the given point. • 3) Find the point of intersection between the two lines. • 4) Use the distance formula to find the distance between the given point and intersection.

  6. Example 2 • Line s contains points (0,0) and (-5,5). Find the distance between line s and point V(1,5)

  7. The distance between two parallel lines is the perpendicular distance between one of the lines and any point on the other line. • Theorem 3.9: In a plane, if two are lines are equidistant from a third line, then the two lines are parallel to each other.

  8. Steps to find distance between two parallel lines. • 1. Write an equation for a line perpendicular to the parallel lines. Use the same y-intercept as a given line. • 2. Solve a system of equation to find the perpendicular line intersects the other line. • 3. Use the distance formula to find the distance between the points of intersection.

  9. Example 3 • Find the distance between the parallel lines a and b with equations y= 2x +3 and y =2x -1

  10. Homework • Page 218: 9-27 odds

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