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Chapter 3: Problem 5

Plot the given points. $$A(2,7), B(-1,-2), C(-4,2), D(0,4)$$

Short Answer

Expert verified
Plot points A, B, C, and D on a coordinate grid following the described steps.

Step by step solution

01

Understand the coordinate system

The coordinate system consists of a horizontal x-axis and a vertical y-axis. Points are represented as \((x, y)\), where \(x\) is the horizontal position and \(y\) is the vertical position.
02

Plot point A(2,7)

Start at the origin \((0,0)\). Move 2 units to the right on the x-axis and 7 units up on the y-axis to locate point A. Mark this point on the graph.
03

Plot point B(-1,-2)

From the origin \((0,0)\), move 1 unit to the left on the x-axis and 2 units down on the y-axis to find point B. Mark this point on the graph.
04

Plot point C(-4,2)

Starting at \((0,0)\), move 4 units to the left on the x-axis and 2 units up on the y-axis to locate point C. Place a point at this location on the graph.
05

Plot point D(0,4)

From the origin \((0,0)\), move directly up 4 units along the y-axis since the x-coordinate is 0, indicating the point is directly above the origin. Mark this point on the graph.

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Key Concepts

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

Plotting Points
Plotting points on a coordinate system is a fundamental skill in math. This involves placing points on a graph, represented by their coordinates, usually written as \( (x, y) \). The first value, \( x \), tells you how far to move horizontally, while the second value, \( y \), indicates the vertical movement. When plotting points:
  • Start from the origin \( (0, 0) \), which is where the x-axis and y-axis intersect.
  • Follow the x-coordinate direction first: move right for positive x values and left for negative x values.
  • Next, adjust vertically based on the y-coordinate: move up for positive y values and down for negative y values.
  • Mark the location on the graph where both movements meet, placing a dot to represent the point.
By practicing plotting various points, you can better understand how coordinates control point placement within the coordinate system.
X-Axis
The x-axis is an essential component of the coordinate system. It is the horizontal line that stretches infinitely to the left and right from the origin. Here are a few key points about the x-axis:
  • It is used to measure the horizontal position of points in the coordinate plane.
  • Points to the right of the origin have positive x-coordinates, while points to the left have negative x-coordinates.
  • Moving along the x-axis helps to determine the first part of each point's coordinate pair.
To plot a point, always begin your movement from the origin along the x-axis, following the sign and magnitude of the x-coordinate. This step is crucial because it sets the starting line for moving vertically to complete the point's placement.
Y-Axis
The y-axis is the vertical counterpart to the x-axis in the coordinate system. Understanding its role is crucial for accurately plotting points. Here鈥檚 what you need to know about the y-axis:
  • It runs vertically, intersecting the x-axis at the origin \( (0, 0) \).
  • The y-axis is used to measure how high or low a point is, based on the y-coordinate of its pair.
  • If a point has a positive y-coordinate, you move upwards from the x-axis. A negative y-coordinate means moving downwards.
  • The position along the y-axis helps determine the second part of each point's coordinate.
Always use the y-axis as a guide to finalize the placement of points after you've determined the horizontal starting position with the x-axis. Together, these two axes form the framework for the entire coordinate plane.

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Most popular questions from this chapter

Use the following table, which gives the fraction (as a decimal) of the total heating load of a certain system that will be supplied by a solar collector of area \(A\) (in \(\mathrm{m}^{2}\) ). Find the indicated values by linear interpolation. $$\begin{array}{l|c|c|c|c|c|c|c}f & 0.22 & 0.30 & 0.37 & 0.44 & 0.50 & 0.56 & 0.61 \\\\\hline A\left(\mathrm{m}^{2}\right) & 20 & 30 & 40 & 50 & 60 & 70 & 80\end{array}$$. For \(f=0.27,\) find \(A\).

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