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Understanding Distance and Midpoint Formulas: Definitions, Examples, and Practice Problems

This guide covers the essential distance and midpoint formulas used to calculate the distance between two points and find the midpoint on a coordinate plane. It provides a step-by-step explanation of the formulas, including practical examples such as calculating distances between points and determining midpoints. Additionally, practice problems are included to reinforce understanding. Whether you're studying for a quiz or enhancing your geometry skills, this resource is your comprehensive tool for mastering distance and midpoint calculations.

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Understanding Distance and Midpoint Formulas: Definitions, Examples, and Practice Problems

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  1. 11.5 Distance & Midpoint Formulas 1 Definitions 2 Formulas & Examples 3 Practice Problems

  2. Distance Formula • Distance between 2 points • Steps • Label Point 1 • Label point 2 • Determine (x1, y1) • Determine (x2, y2) • Substitute into • Solve 2 (x2,y2) distance 1 (x1,y1)

  3. Distance Example Find the distance between the points at (2,3) and (-4,6) 1 2 (x1,y1) (x2,y2)

  4. Another Distance Example Tracey hits a golf ball that lands 20 feet short and 8 feet to the right of the cup. On her first putt, the ball lands 2 feet to the left and 3 feet beyond the cup. Assuming the ball travelled in a straight line, determine how far it travelled. 2 (-2,3) (x2,y2) 1 (8,-20) (x1,y1)

  5. Midpoint Formula • Exact center between 2 points • Steps • Label Point 1 • Label point 2 • Determine (x1, y1) • Determine (x2, y2) • Substitute into • Solve 2 Midpoint (x2,y2) 1 (x1,y1)

  6. Midpoint Example Find the midpoint between the points at (2,3) and (-4,6) 1 2 (x1,y1) (x2,y2)

  7. Practice Problems • Page 613 Problems 13-26, distance and midpoint Even due today Odd due next class

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