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Warm Up

Warm Up. Find the distance between (2, 4) and (6, -8) Find the midpoint of the above line. 3D Coordinates. Coordinates in 2 Dimensions. (3,2). y. 2. x. 3. The 3 rd Dimension. z. (3,2,4). 4. y. (3,2,0). 2. x. 3.

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Warm Up

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  1. Warm Up Find the distance between (2, 4) and (6, -8) Find the midpoint of the above line.

  2. 3D Coordinates

  3. Coordinates in 2 Dimensions (3,2) y 2 x 3

  4. The 3rd Dimension z (3,2,4) 4 y (3,2,0) 2 x 3

  5. A three-dimensional coordinate system or 3-space, is formed by the intersection of an x-axis, a y-axis and a z-axis. Three Planes: xy-plane, xz-plane, yz-plane Divide 3-D Space into 8 OCTANTS Ordered triple (x, y, z) z A(-2,-3,1) y x B(0,2,-2)

  6. Consider the Point A(5,4,2) C B D G E F

  7. A(2,4,0) B(0,4,3) C(2,4,3) D(2,0,3)

  8. Distance and Midpoint Formula in a 3-Dimensions

  9. Distance and Midpoint Formulas in 3-D Distance between

  10. Use the formula to find the distance and midpoint between the points shown on the diagram (2, -3, 3) (1, 0, -2) 3-D distance calculator

  11. Recognize and graph the equation of a plane - 3x + 2y + 4z = 12 • Find intersection points with the axes by setting the other coordinates equal to zero. (Ex. When looking for the intersection of the x-axis, plug zero in for y and z.) • Plot and connect the points. • Shade the region.

  12. Write an equation for a sphere Write an equation of a sphere in standard form with center (1, 5, -3) and radius r = 5 Write the standard form for the equation of a sphere:

  13. Homework/Classwork Workbook Page 233: 1-16 (omit 4-6 and 11 & 12) Find the distance and midpoint for 7-10.

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