Exercise 56 Page 582

Practice makes perfect

a Let's begin by copying the table and filling out the three first columns.

1^{st} point 2^{nd} point 3^{rd} point 4^{th} point P o i n t s o n t h e x - a x i s (- 3, 0, 0) (- 2, 0, 0) (- 1, 0, 0) (2, 0, 0) P o i n t s o n t h e y - a x i s (0, - 3, 0) (0, - 2, 0) (0, 1, 0) (0, 2, 0) P o i n t s o n t h e z - a x i s (0, 0, - 4) (0, 0, - 2) (0, 0, 1) (0, 0, 2) P o i n t s n o t o n t h e x -, y -, o r z - a x i s

Next, we will plot these coordinates in a

x y z -

coordinate system.

Let's also choose some points that are not on any of the axis.

1^{st} point 2^{nd} point 3^{rd} point 4^{th} point P o i n t s o n t h e x - a x i s (- 3, 0, 0) (- 2, 0, 0) (- 1, 0, 0) (2, 0, 0) P o i n t s o n t h e y - a x i s (0, - 3, 0) (0, - 2, 0) (0, 1, 0) (0, 2, 0) P o i n t s o n t h e z - a x i s (0, 0, - 4) (0, 0, - 2) (0, 0, 1) (0, 0, 2) P o i n t s n o t o n t h e x -, y -, o r z - a x i s (4, 4, 4) (- 2, 2, 4) (- 1, 1, 1) (1, - 4, 5)

Let's graph them in a

x y z -

coordinate system.

As we can see, the coordinates on the $x -$ axis have $y -$ and $z -$ coordinates that are both equal to $0 .$

b Based on the table from Part A, we can conjecture that if a point lies on an axis, the values of the other axes are zero.

11.2.1 Creating a Three-Dimensional Model p.582-583

11.2.2 Graphing Equations in Three Dimensions p.586-587

11.2.3 Solving Systems of Three Equations with Three Variables p.590-592

11.2.4 Using Systems of Three Equations for Curve Fitting p.598-600

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