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Understanding Distance Formula and Circle Equations in Coordinate Geometry

This guide explores key concepts in coordinate geometry, including how to calculate the distance between points using the distance formula. It provides examples for finding the distance between points such as (-4, 2) and (2, -1), as well as writing the equation of a circle with given center and radius. Additionally, it discusses slopes of lines, determining whether lines are parallel or perpendicular, and introduces the midpoint formula. Perfect for students looking to grasp the fundamentals of distance, circles, and slopes in geometry.

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Understanding Distance Formula and Circle Equations in Coordinate Geometry

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  1. 13.1 Cooridinate Geometry

  2. Distance Formula: Example: Find the distance between (-4,2) (2,-1)

  3. The equation________________________ ___________________________________ ___________________________________ Example: Write the equation of a circle if the center is (2,-1) and it has a radius of 4.

  4. Find the distance between the following sets of points. • (-1,2) (7,5) • (-4, -1) (2,-3) • (-3,3) (3,-3)

  5. Find the center and the length of the radius of the circle with the equation of: Find the equation of the circle with a center at (j, -1) and a radius =

  6. 13.2 and 13.3 Slope of a line

  7. or _________________________________

  8. Slope can either be: • ___________________________ • ___________________________ • ___________________________ • ___________________________

  9. Parallel: ____________________________ • ____________________________________ • ___________________________________ • ____________________________________ • ____________________________________ • Perpendicular: ______________________ • ____________________________________ • ____________________________________ • ____________________________________

  10. Refresher: The equation of a line is:

  11. Find the slopes of the lines containing these points. • (3,-1) (5,4) • (-2,5) (7,2) • (3,3) (3,7)

  12. Tell whether the lines are parallel, perpendicular or intersecting given the there slopes. • m=3/4 and m=12/16 • m= -3/4 and m=4/3 • m= 3 and m= -3

  13. Given Points E(-4,1) F(2,3) G(4,9) and H(-2,7). Prove the shape is a rhombus.

  14. 13.5 Midpoint Formula

  15. Midpoint Formula: _______________________ • _________________________________________ • _________________________________________ • ________________________________________ • _________________________________________ • _________________________________________ • _________________________________________

  16. Find the Midpoint of the segment that joins (-11,3) and (8,-7)

  17. Given the points A(2,1) and B(8,5) show that P(3,6) is on the perpendicular bisector of AB. • First find the MP of AB • Then find the slope of the MP and P. • Compare it to the slope of AB

  18. Find the length, slope and MP of PQ: • P(-3,4) Q(7,8) • P(-7,11) Q(1,-4)

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