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5.6: The Distance Formula
5.6: The Distance Formula andthe Method of Quadrature
Expectation:
G1.1.5: Given a line segment in terms of itsendpoints in the coordinate plane, determine itslength and midpoint.
3/15/2016
5.6: The Distance Formula
Without looking in your book,determine the distance between 2points with coordinates (x1, y1) and(x2, y2).
3/15/2016
5.6: The Distance Formula
3/15/2016
5.6: The Distance Formula
The distance formula
In a coordinate plane, the distance, d,between points (x1, y1) and (x2, y2) isgiven by the following formula:
3/15/2016
5.6: The Distance Formula
An airplane is 25 miles north and 50miles east of the airport. Another planeis 30 miles west and 15 miles south ofthe airport. What is the grounddistance between the 2 planes?
What is the distance in the standard (x,y)coordinate plane between the points (0,1)and (4,4)?
A.√7
B.3
C.4
D.5
E.√27
3/15/2016
5.6: The Distance Formula
3/15/2016
5.6: The Distance Formula
The Method of Quadrature
Quadrature is a method of estimating thearea under a curve using the sum of theareas of rectangles.
3/15/2016
5.6: The Distance Formula
Estimating the area between y = -x2 + 9and y = 0 for -3 ≤ x ≤ 3.
1. Graph y = -x2 + 9
2. Form rectangles 1 unit wide with theupper left hand vertex touching thegraph.
3. Determine the area of each rectangle.
4. Find the sum of all areas.
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5.6: The Distance Formula
Estimating the Area of a Circle
1. Draw a 90° sector of a circle withradius 6.
2. Form rectangles 1 unit wide with theupper left hand vertex touching thegraph (left hand rule).
3. Find the area of each rectangle (usepyth. thm to find y)
3/15/2016
5.6: The Distance Formula
Estimating the Area of a Circle
4. Find the sum of the areas of therectangles.
5. Multiply by 4 to estimate the area ofthe entire circle.
6. Is your estimate too high or too low?
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5.6: The Distance Formula
Estimating the Area of a Circle
Redraw the sector of the circle.
8. Form rectangles 1 unit wide with theupper right hand vertex touching thegraph (right hand rule).
9. Find the area of each rectangle (usepyth. thm to find y).
10. Find the sum of the areas of therectangles.
3/15/2016
5.6: The Distance Formula
Estimating the Area of a Circle
11. Multiply by 4 to estimate the area ofthe entire circle.
12. Is your estimate too high or too low?
3/15/2016
5.6: The Distance Formula
Estimating the Area of a Circle
13. Find the average of your first twoestimates.
14. Which estimate is the most accurate:left hand rule, right hand rule or theaverage?
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5.6: The Distance Formula
Estimate the area between the x-axisand y=x for 0 ≤ x ≤ 5.
3/15/2016
5.6: The Distance Formula
Assignment
pages 343-345, numbers 10-18(evens), 21, 24, 28, 30-37, 39, 40