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5.6: The Distance Formula and the Method of Quadrature

5.6: The Distance Formula and the Method of Quadrature. Expectation: G1.1.5: Given a line segment in terms of its endpoints in the coordinate plane, determine its length and midpoint.

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5.6: The Distance Formula and the Method of Quadrature

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  1. 5.6: The Distance Formula and the Method of Quadrature Expectation: G1.1.5: Given a line segment in terms of its endpoints in the coordinate plane, determine its length and midpoint. 5.6: The Distance Formula

  2. Without looking in your book, determine the distance between 2 points with coordinates (x1, y1) and (x2, y2). 5.6: The Distance Formula

  3. 5.6: The Distance Formula

  4. The distance formula • In a coordinate plane, the distance, d, between points (x1, y1) and (x2, y2) is given by the following formula: 5.6: The Distance Formula

  5. An airplane is 25 miles north and 50 miles east of the airport. Another plane is 30 miles west and 15 miles south of the airport. What is the ground distance between the 2 planes? 5.6: The Distance Formula

  6. What is the distance in the standard (x,y) coordinate plane between the points (0,1) and (4,4)? • √7 • 3 • 4 • 5 • √27 5.6: The Distance Formula

  7. The Method of Quadrature • Quadrature is a method of estimating the area under a curve using the sum of the areas of rectangles. 5.6: The Distance Formula

  8. Estimating the area between y = -x2 + 9 and y = 0 for -3 ≤ x ≤ 3. • 1. Graph y = -x2 + 9 • 2. Form rectangles 1 unit wide with the upper left hand vertex touching the graph. • 3. Determine the area of each rectangle. • 4. Find the sum of all areas. 5.6: The Distance Formula

  9. Estimating the Area of a Circle • 1. Draw a 90° sector of a circle with radius 6. • 2. Form rectangles 1 unit wide with the upper left hand vertex touching the graph (left hand rule). • 3. Find the area of each rectangle (use pyth. thm to find y) 5.6: The Distance Formula

  10. Estimating the Area of a Circle • 4. Find the sum of the areas of the rectangles. • 5. Multiply by 4 to estimate the area of the entire circle. • 6. Is your estimate too high or too low? 5.6: The Distance Formula

  11. Estimating the Area of a Circle • Redraw the sector of the circle. • 8. Form rectangles 1 unit wide with the upper right hand vertex touching the graph (right hand rule). • 9. Find the area of each rectangle (use pyth. thm to find y). • 10. Find the sum of the areas of the rectangles. 5.6: The Distance Formula

  12. Estimating the Area of a Circle • 11. Multiply by 4 to estimate the area of the entire circle. • 12. Is your estimate too high or too low? 5.6: The Distance Formula

  13. Estimating the Area of a Circle • 13. Find the average of your first two estimates. • 14. Which estimate is the most accurate: left hand rule, right hand rule or the average? 5.6: The Distance Formula

  14. Estimate the area between the x-axis and y=x for 0 ≤ x ≤ 5. 5.6: The Distance Formula

  15. Assignment • pages 343-345, numbers 10-18 (evens), 21, 24, 28, 30-37, 39, 40 5.6: The Distance Formula

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