11.9 Three dimensional Coordinates
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1 11.9 Three dimensional Coordinates Apr 1 10:06 AM 1
2 A Three Dimensional Coordinate System Dec 9 5:26 PM 2
3 With an ordered triple (x, y, z) Dec 9 5:26 PM 3
4 x axis y axis z axis Dec 9 5:26 PM 4
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9 Circle Dec 9 5:27 PM 9
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17 2. Because we moved 3 units on the x axis and then up 4 units of the y axis this is how many dimensions? TWO DIMENSIONS! 3. If an object is hanging from the ceiling, how can we identify its position from the classroom door? Apr 1 10:11 AM 17
18 4. This object hanging in space is in what dimension? 3RD DIMENSION! 5. If we have two axes in a two dimension plane, (the x and y coordinate plane), how many are we going to have in a three dimension plane? 3 AXES! 6. The names of the three axes in a three dimension plane are X, Y, and Z. Apr 1 10:18 AM 18
19 7. Draw a three dimension coordinate system and identify the x, y, z axis. 8. Graph the ordered triple (4, 5, and 3) above. Label point A. 9. Graph the ordered triple ( 2, 4, 5) above. Label point B. 10. Graph the ordered triple (3, 2, 6) above. Label point C. Apr 1 10:20 AM 19
20 11. The distance formula between two points on a two dimensional graph is:. 12. The three dimensional distance formula is as follows:. Apr 1 10:20 AM 20
21 13. Find the distance between points a and b where a = ( 5, 2, 1) and b = (4, 0, 3). Apr 1 10:22 AM 21
22 14. If a box has the dimensions of 7 x 2 x 6. Draw a picture of this box and put the dimensions in. Where is the longest distance inside your box? Identify it with two different letters. This distance can be calculated by using the following formula: What is that distance for this particular box? Apr 1 10:22 AM 22
23 15. If a circle has a radius of 5 and its center is located at the ordered pair (4, 2), write its equation:. Write the general formula equation for a circle:. Apr 1 10:23 AM 23
24 16. Because a sphere is a 3 D figure, and is made up of points equal distance from a center point, the equation for the sphere is almost identical to that of a circle. In a circle, the center is located at the points (h, k). In a sphere the center is located at the points (h, k, j), where j accommodates that third dimension. The Radius r is still the representation for the distance from the center of a circle to the edge. The equation of a sphere is as follows:. Apr 1 10:24 AM 24
25 Write an equation for a sphere with a center at (4, 3, 5) and a radius 7. Apr 1 10:25 AM 25
26 If the equation of a sphere is as follows: (x 1) 2 + (y + 3) 2 + (z 4) 2 = 36. What is the center of the circle? The radius value?. Apr 1 10:26 AM 26
27 1. If the center of a sphere has an ordered triple of (2, 4, 6) and a point on the outside edge has an ordered triple of ( 1, 3, 8). Apr 1 10:27 AM 27
28 The midpoint of a 3 D object can be found by the following formula:. Find the above midpoint. between (2, 4, 6) and ( 1, 3, 8). Apr 1 10:27 AM 28
29 Chapter 11 WS A's pdf Dec 10 2:25 PM 29
30 Chapter 11 WS A's KEY.pdf Dec 10 2:25 PM 30
31 Dec 11 9:04 PM 31
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50 Review Only Dec 10 2:28 PM 50
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55 1. Draw a coordinate graph and graph the order pair ( 3, 4). Apr 1 10:11 AM 55
56 Attachments Chapter 11 WS A's pdf Chapter 11 WS A's KEY.pdf
a. Plot the point (x, y, z) and understand it as a vertex of a rectangular prism. c. Recognize and understand equations of planes and spheres.
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= 2x c 2 x 2cx +6x+9 = c 2 x. Thus we want (2c +6)x 2 +9x=c 2 x. 2c+6=0and9 c 2 =0. c= 3
CD EXAM WITH PROOFS. For what value(s) of the number a do the equations x ax + = 0 x x+a = 0 have a common real solution? Proof. Let z be a common real solution. Then z az + = z z+a=0 ( a)z = a a = or
We have already studied equations of the line. There are several forms:
Chapter 13-Coordinate Geometry extended. 13.1 Graphing equations We have already studied equations of the line. There are several forms: slope-intercept y = mx + b point-slope y - y1=m(x - x1) standard