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Chapter 3: Problem 37

In Exercises \(31-40,\) use a grid 10 squares wide and 10 squares high to plot the given coordinates. Choose your scale carefully. Scales may vary. (-100,-5),(350,20),(800,37)

Short Answer

Expert verified
Scale: x-axis 100 units/square, y-axis 5 units/square. Points: (-100,-5), (350,20), (800,37).

Step by step solution

01

Understand the Grid

You have a grid that is 10 squares wide and 10 squares high. This means you need to plot coordinates within a 10x10 section.
02

Choose a Scale

Consider the range of your coordinates. The x-values range from -100 to 800, and the y-values range from -5 to 37. A suitable scale could be: 1 square on the grid corresponds to 100 units on the x-axis and 5 units on the y-axis.
03

Label the Axes

Draw and label the x-axis and y-axis with your chosen scale. For example, on the x-axis mark every square as -100, 0, 100, 200, etc., up to 800. On the y-axis, mark every square as -5, 0, 5, 10, etc., up to 50.
04

Plot the Point (-100, -5)

Locate -100 on the x-axis and -5 on the y-axis. Since -100 and -5 correspond exactly to one square on the grid, plot the point at the bottom-left corner of the grid.
05

Plot the Point (350, 20)

Locate 350 on the x-axis and 20 on the y-axis. On your grid, move 3.5 squares to the right from the origin and 4 squares up. Plot the point accordingly.
06

Plot the Point (800, 37)

Locate 800 on the x-axis and 37 on the y-axis. On your grid, move 8 squares to the right from the origin and 7.4 squares up. Plot the point accordingly.
07

Verify the Points

Double-check the plotted points to ensure they match the given coordinates considering the chosen scale.

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Key Concepts

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

Scale Selection
When plotting coordinates on a grid, choosing the right scale is essential. A scale determines how to represent numerical values. For this exercise, the x-values range from -100 to 800 and the y-values from -5 to 37. Our grid is 10 squares wide and 10 squares high. To fit all points conveniently, select a scale that makes the numbers manageable.
Given the ranges:
  • x-axis: -100 to 800
  • y-axis: -5 to 37
A suitable scale could be:
  • 1 square = 100 units on the x-axis
  • 1 square = 5 units on the y-axis
This helps in evenly distributing the points and fitting them within the grid dimensions.
Grid Plotting
After choosing a scale, the next step is plotting the points on the grid. Here鈥檚 how you do it:
1. Divide the grid into equal increments based on the chosen scale. For instance, each square might represent 100 units on the x-axis and 5 units on the y-axis.
2. Locate the points along the axes. For example, the point (-100, -5) is exactly one square to the left on the x-axis and one square down on the y-axis.
  • Point (-100, -5): Move 1 square left and 1 square down.
  • Point (350, 20): Move 3.5 squares right and 4 squares up.
  • Point (800, 37): Move 8 squares right and 7.4 squares up.
Plot the points accordingly and mark them on the grid.
Labeling Axes
Correctly labeling the axes is crucial for clarity. Here鈥檚 how to do it:
1. Draw the x-axis and y-axis intersecting at the origin (0,0).
2. Based on the scale, mark the axes at regular intervals.
  • For the x-axis, you might label: -100, 0, 100, 200, ..., 800.
  • For the y-axis, you might label: -5, 0, 5, 10, ..., 50.
Clearly marked axes help in understanding the position of each point and in verifying that the scales have been applied correctly.
Verifying Points
Lastly, verifying the points ensures accuracy. Here鈥檚 how to check if the points are plotted correctly:
1. Revisit each point and confirm their positions with respect to the scale.
  • For (-100, -5): Check if it's 1 square left and 1 square down.
  • For (350, 20): Confirm it鈥檚 3.5 squares right and 4 squares up.
  • For (800, 37): Ensure it's 8 squares right and 7.4 squares up.
2. Cross-check the plotted points with the coordinates to confirm accuracy. This step is crucial because a small error in plotting might lead to incorrect results. Accurate verification helps in ensuring the plotted graph is reliable.

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