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Chapter 6: Problem 2

When stating the coordinates of a point, which coordinate is given first?

Short Answer

Expert verified
Answer: The x-coordinate is given first when stating the coordinates of a point in both 2D and 3D coordinate systems.

Step by step solution

01

Identify the Coordinate System

Before identifying which coordinate is given first, we must decide whether the point is in a two-dimensional (2D) or a three-dimensional (3D) coordinate system. In a 2D coordinate system, we have two coordinates (x and y), while in a 3D coordinate system, we have three coordinates (x, y, and z).
02

The Order of Coordinates in a 2D Coordinate System

In a 2D coordinate system, a point is represented by the coordinates (x, y). Here, the x-coordinate is given first, followed by the y-coordinate. For example, if you have coordinates (3, 2), the x-coordinate is 3, and the y-coordinate is 2.
03

The Order of Coordinates in a 3D Coordinate System

In a 3D coordinate system, a point is represented by the coordinates (x, y, z). Similar to the 2D coordinate system, the x-coordinate is given first, followed by the y-coordinate and the z-coordinate. For example, if you have coordinates (4, -1, 6), the x-coordinate is 4, the y-coordinate is -1, and the z-coordinate is 6.
04

Conclusion

In both 2D and 3D coordinate systems, the x-coordinate is given first when stating the coordinates of a point. This is the standard convention adopted in mathematics and physics.

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Most popular questions from this chapter

Plot a graph of the following functions. In each case state the domain and the range of the function. (a) \(f(x)=3 x+2,-2 \leq x \leq 5\) (b) \(g(x)=x^{2}+4,-2 \leq x \leq 3\) (c) \(p(t)=2 t^{2}+8,-2 \leq t \leq 4\) (d) \(f(t)=6-t^{2}, 1 \leq t \leq 5\)

By sketching a graph of \(y=3 x-1\) show that this is a one-to-one function.

Calculate \(f(x+h)\) when (a) \(f(x)=x^{2}\) (b) \(f(x)=x^{3}\) (c) \(f(x)=\frac{1}{x}\) In each case write down the corresponding expression for \(f(x+h)-f(x)\).

Explain the meaning of an expression such as \(y(x)\) in the context of functions. What is the interpretation of \(x(t) ?\)

Study graphs of the functions \(y=x^{2}\) and \(y=-x^{2}\). Are these continuous functions?
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