5.6: The Distance Formula and the Method of Quadrature

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.

2

• Without looking in your book, determine the
  distance between 2 points with coordinates (x1,
  y1) and (x2, y2).

3
(No Transcript)
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

• 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?

6

• What is the distance in the standard (x,y)
  coordinate plane between the points (0,1) and
  (4,4)?
• v7
• 3
• 4
• 5
• v27

7
The Method of Quadrature

• Quadrature is a method of estimating the area
  under a curve using the sum of the areas of
  rectangles.

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.

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)

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?

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.

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?

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?

14

• Estimate the area between the x-axis and yx for
  0 x 5.

15
Assignment

• pages 343-345, numbers 10-18 (evens), 21, 24, 28,
  30-37, 39, 40