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9.1/9.2 Distance/Midpoint Formulas and Circles

Learn to find distances, midpoints, write equations, and graph circles using distance and midpoint formulas. Practice examples provided for understanding.

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9.1/9.2 Distance/Midpoint Formulas and Circles

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  1. 9.1/9.2 Distance/Midpoint Formulas and Circles Students will be able to find the distance between two points and the midpoint of the segment joining them. Students will be able to write equations and graph circles.

  2. Distance formula

  3. Midpoint formula

  4. Example 1 Find the length of the segment joining the points (-4,-10) and (-3,-12).

  5. Example 2 Find the coordinates of the midpoint of the segment joining the points (-17,12) and (9, -11).

  6. circle • A circle is the set of all points in a plane that are a fixed distance, called the radius, from a fixed point, called the center. • A circle with center (h,k) and radius r has the equation:

  7. Example 3 Write the equation of a circle with center (2,-5) and radius 3.

  8. Example 4 Graph

  9. Example 5 If the graph of the given equation is a circle, find its center and radius. If the equation has no graph, say so.

  10. Example 6 If the graph of the given equation is a circle, find its center and radius. If the equation has no graph, say so.

  11. Example 7 Find the equation of a circle with radius 3 and has its center in the first quadrant and is tangent to the y-axis at (0,2).

  12. Homework Page 410 #2-24 even

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