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Chapter 3: Problem 19

Plot each point in a rectangular coordinate system. $$ (-2,4) $$

Short Answer

Expert verified
Plot point (-2, 4) by moving 2 units left on the x-axis and 4 units up on the y-axis.

Step by step solution

01

- Identify the coordinates

The point given is (-2, 4) . Here, -2 is the x-coordinate and 4 is the y-coordinate.
02

- Locate the x-coordinate

Move left 2 units along the x-axis since the x-coordinate is -2.
03

- Locate the y-coordinate

From the position at -2 on the x-axis, move up 4 units along the y-axis since the y-coordinate is 4.
04

- Plot the point

Mark the point where the coordinates (-2, 4) are located. This is the point where you have moved left 2 units and up 4 units.

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Key Concepts

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

rectangular coordinate system
The rectangular coordinate system is a way to locate points on a plane using two numbers. These numbers are called coordinates. The first number is the x-coordinate, and it tells us how far to move left or right. The second number is the y-coordinate, and it tells us how far to move up or down.

Imagine the plane like a piece of graph paper. The center point, where the x-axis and y-axis cross, is called the origin. The origin has coordinates (0, 0).

When plotting a point, you start at the origin and use the coordinates to find the location of the point.
Other things to remember:
  • The x-axis goes from left to right (horizontally).
  • The y-axis goes from bottom to top (vertically).
This system helps us precisely place points and understand their location on a plane.
x-coordinate
The x-coordinate tells us the point鈥檚 position along the x-axis. In the given example (-2, 4), -2 is the x-coordinate.

Here are some key points about the x-coordinate:
  • A positive x-coordinate means the point is to the right of the origin.
  • A negative x-coordinate means the point is to the left of the origin.
To locate the x-coordinate, start at the origin (0,0) and then move left or right based on the sign and value of the coordinate.

In our example, you start at the origin and move 2 units to the left since -2 is the x-coordinate. This first step helps you find the horizontal position of the point.
y-coordinate
The y-coordinate determines the point鈥檚 position along the y-axis. In our example (-2, 4), 4 is the y-coordinate.

Important points about the y-coordinate:
  • A positive y-coordinate means the point is above the origin.
  • A negative y-coordinate means the point is below the origin.
Just like with the x-coordinate, you start at the origin (0,0) to find the y-coordinate but then move up or down.

From the position where you moved to find the x-coordinate, in our example at -2, you then move 4 units up because 4 is the y-coordinate. This second step completes the process of plotting the point. Now you can mark the point at (-2, 4) on the graph, and you see exactly where it is located.

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Most popular questions from this chapter

Find the \(x\) - and \(y\) -intercepts. Then graph each equation. $$ -\frac{9}{4} y=x $$

The total amount spent on analog TVs in the United States changed from 5836 million dollars in 2003 to 1424 million dollars in \(2006 .\) Find and interpret the average rate of change in sales, in millions of dollars per year. Round your answer to the nearest hundredth. (Source: Consumer Electronics Association.)

Find an equation of the line passing through the given points. (a) Write the equation in standard form. (b) Write the equation in slope-intercept form if possible. $$ \left(-\frac{4}{9},-6\right) \text { and }\left(\frac{12}{7},-6\right) $$

Use your knowledge of the slopes of parallel and perpendicular lines. Is the figure with vertices at \((-11,-5),(-2,-19),(12,-10),\) and \((3,4)\) a parallelogram? Is it a rectangle? (Hint: A rectangle is a parallelogram with a right angle.)

Find an equation of the line that satisfies the given conditions. (a) Write the equation in slope-intercept form. (b) Write the equation in standard form. Through \((2,-7) ;\) perpendicular to \(5 x+2 y=18\)
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