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Chapter 3: Problem 21

plot the given point in a rectangular coordinate system. $$(0,0)$$

Short Answer

Expert verified
The given point (0,0) is marked at the intersection of the X-axis and Y-axis, which is the origin in a rectangular coordinate system.

Step by step solution

01

Understand the Coordinates

Before plotting, it's crucial to understand what the coordinates (0,0) represent. They indicate a point in a two-dimensional space, where the first coordinate (0) is the X-coordinate (horizontal) and the second coordinate (0) is the Y-coordinate (vertical). The point (0,0) is called the origin, the point where both the X-axis and the Y-axis intersect.
02

Draw the Coordinate Axes

Draw two perpendicular lines intersecting each other. The horizontal line is the X-axis and the vertical line is the Y-axis. Make sure to mark the point where they intersect as '0' on both axes.
03

Plot the Point

Since the point to be plotted is (0,0), which is the origin, mark this point as a dot on the intersection of X-axis and Y-axis.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Coordinates
Coordinates are a way to pinpoint the exact location of a point in a two-dimensional space using ordered pairs. In simpler terms, they help us know exactly where a point is on a plain surface. This system consists of two numbers called coordinates. The first coordinate in the pair is the X-coordinate, which shows the horizontal position of the point. The second number is the Y-coordinate, showing the vertical position.
  • The X-coordinate measures how far left or right the point is from the vertical Y-axis.
  • The Y-coordinate measures how far up or down the point is from the horizontal X-axis.
Knowing both coordinates, we can precisely locate any point on the rectangular coordinate system. This makes it easy to plot not just single points, but more complex data sets as well.
Origin
The origin is a special point in the coordinate system. It鈥檚 like the starting point for all your graphing journeys. In a rectangular coordinate system, the origin is where the X-axis and Y-axis meet. It鈥檚 represented by the coordinate (0,0), signaling that it has zero distance from both axes.
  • Think of it as the center or the heart of your grid.
  • The origin is important because it gives us a reference point for plotting other coordinates.
Without the origin, it would be tricky to determine how far along or up a point is on either axis. Understanding the origin helps us interpret the distance and direction of other points relative to this central position.
Plotting Points
Plotting points in the rectangular coordinate system is key to understanding how different points relate to one another spatially. By plotting a point, you visually represent its position based on its coordinates. To do this: 1. Start by locating the X-coordinate on the horizontal axis. 2. Move vertically to the Y-coordinate. Mark this intersection point with a dot.
  • In cases where the point is at the origin, as in (0,0), you do not need to move along the axes since it's already centered.
  • This simple method lays the groundwork for more complex graphing tasks, such as plotting functions or creating geometrical shapes.
Plotting helps us turn abstract numerical data into clear, visual information, making it easier to see patterns and relationships between points.

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Most popular questions from this chapter

a. Graph each of the following points: $$ \left(1, \frac{1}{2}\right),(2,1),\left(3, \frac{3}{2}\right),(4,2) $$ Parts (b)-(d) can be answered by changing the sign of one or both coordinates of the points in part (a). b. What must be done to the coordinates so that the resulting graph is a mirror-image reflection about the \(y\) -axis of your graph in part (a)? c. What must be done to the coordinates so that the resulting graph is a mirror-image reflection about the \(x\) -axis of your graph in part (a)? d. What must be done to the coordinates so that the resulting graph is a straight-line extension of your graph in part (a)?

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I have less than \(\$ 5.00\) in nickels and dimes, so the linear inequality $$0.05 n+0.10 d<5.00$$ models how many nickels, \(n,\) and how many dimes, \(d,\) that I might have.

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. The inequality \(2 x-3 y<6\) contains a "less than" symbol, so its graph lies below the boundary line.

Describe the graph of \(x=-100\).

Use a graphing utility to graph each equation. You will need to solve the equation for \(y\) before entering it. Use the graph displayed on the screen to identify the \(x\)-intercept and the \(y\)-intercept. \(2 x+y=4\)
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