6.4: Coordinates in Three Dimensions

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6.4: Coordinates in Three Dimensions 3/25/2017 6.4: Coordinates in 3 Dimensions

What is the sum of the 2 real solutions to the equation x = 6 – x2? 1 -1 -6

Three Dimensional Coordinates x-axis, y-axis, z-axis. (x,y,z) ordered triples. 3/25/2017 6.4: Coordinates in 3 Dimensions

3 Dimensional Coordinate System z y x 3/25/2017 6.4: Coordinates in 3 Dimensions

6.4: Coordinates in 3 Dimensions Plot (3,2,5) 3/25/2017 6.4: Coordinates in 3 Dimensions

6.4: Coordinates in 3 Dimensions Plot (-4,-1,2) 3/25/2017 6.4: Coordinates in 3 Dimensions

6.4: Coordinates in 3 Dimensions Plot (0,5,-4) 3/25/2017 6.4: Coordinates in 3 Dimensions

6.4: Coordinates in 3 Dimensions Coordinate Planes There are 3 coordinate planes in a 3 dimensional coordinate system. They are the xy plane, the yz plane and the xz plane. In the xy plane, the z coordinate of all points is 0. In the yz plane the x coordinate of all points is 0. In the xz plane the y coordinate of all points is 0. 3/25/2017 6.4: Coordinates in 3 Dimensions

6.4: Coordinates in 3 Dimensions Octants The xy, yz and xz planes split space into 8 regions called octants. The only octant that has a specific name is the region in which all 3 coordinates are positive. This octant is called the first octant. 3/25/2017 6.4: Coordinates in 3 Dimensions

6.4: Coordinates in 3 Dimensions Octants The other 7 octants are called out by location i.e. top back right or bottom front left. 3/25/2017 6.4: Coordinates in 3 Dimensions

Give the location (octant) of: (-4,9,8) Back, right, top (3,9,0) xy plane (-4, -8,-1) Back, left, bottom 3/25/2017 6.4: Coordinates in 3 Dimensions

Give the coordinates of a point: In the bottom back right octant. In the top front left octant In the xz coordinate plane. 3/25/2017 6.4: Coordinates in 3 Dimensions

Distance Formula in Three Dimensions The distance d between the points (x1,y1,z1) and (x2,y2,z2) is given by d= 3/25/2017 6.4: Coordinates in 3 Dimensions

6.4: Coordinates in 3 Dimensions Calculate the distance between (3,6,9) and (2,4,-8). 3/25/2017 6.4: Coordinates in 3 Dimensions

Give the coordinates of 2 points that are 10 units apart in the 3-d coordinate system.

6.4: Coordinates in 3 Dimensions 3-D Midpoint Formula If A(x1,y1,z1) and B(x2,y2,z2), then the coordinates of the midpoint, M, of AB are given by the formula: M = x1+x2 , y1+y2 , z1+z2 2 3/25/2017 6.4: Coordinates in 3 Dimensions

6.4: Coordinates in 3 Dimensions What are the coordinates of the midpoint of the segment determined by (-2,4,3) and (8, 12,-9)? 3/25/2017 6.4: Coordinates in 3 Dimensions

6.4: Coordinates in 3 Dimensions Assignment pages 399-400, # 14 - 48(evens) 3/25/2017 6.4: Coordinates in 3 Dimensions