Question

. Denise plots the data on a coordinate grid. She begins by plotting the data for Week 3 and Week 11. What are the coordinates of the two points that Denise plots? (A) \((11,3)\) and \((11.5,4.7)\) (B) \((3,11)\) and \((4.7,11.5)\) (C) \((3,4.7)\) and \((11,11.5)\) (D) \((4.7,3)\) and \((11.5,11)\)

Short answer

The coordinates of the two points that Denise plots are (C) \((3,4.7)\) and \((11,11.5)\).

Step-by-step solution

Understand the coordinate format

Coordinates on a grid are given as (x, y), where x represents the horizontal position and y represents the vertical position on the grid.

Analyze Option (A)

In option (A), the coordinates are given as \((11,3)\) and \((11.5,4.7)\). It suggests that during Week 3, the x-coordinate is 11, which does not make sense as Week 3 should have an x-coordinate of 3. Therefore, this option is incorrect.

Analyze Option (B)

In option (B), the coordinates are given as \((3,11)\) and \((4.7,11.5)\). This suggests that during Week 3, the x-coordinate is 3, which seems correct. However, the data for Week 11 has the x-coordinate as 4.7, which is also incorrect. Therefore, this option is incorrect.

Analyze Option (C)

In option (C), the coordinates are given as \((3,4.7)\) and \((11,11.5)\). This suggests that during Week 3, the x-coordinate is 3, and during Week 11, the x-coordinate is 11. This option seems correct, as both weeks have their respective x-coordinates.

Analyze Option (D)

In option (D), the coordinates are given as \((4.7,3)\) and \((11.5,11)\). It suggests that during Week 3, the x-coordinate is 4.7, which does not make sense as Week 3 should have an x-coordinate of 3. Therefore, this option is incorrect.

Conclusion

Based on our analysis, the correct coordinates of the two points that Denise plots are given in option (C): \((3,4.7)\) and \((11,11.5)\).

Key concepts

Cartesian Coordinate System

Understanding the Cartesian coordinate system is foundational when it comes to graphing data. This system is a two-dimensional plane made up of a horizontal axis (x-axis) and a vertical axis (y-axis). Each point on this plane can be described by an ordered pair of numbers known as coordinates. The first number in the pair, the x-coordinate, indicates the point's horizontal position, while the second number, the y-coordinate, determines the vertical position.

When plotting points like Denise did for Week 3 and Week 11, it's crucial to identify the correct sequence of the x and y values. For example, if we represent the weeks on the x-axis and the data values on the y-axis, the point for Week 3 will have 3 as its x-coordinate, not 11. Visualizing a grid and labeling it correctly can prevent confusion and help ensure accurate plotting.

Data Representation

Data representation on a coordinate grid allows us to visualize and interpret information effectively. It's a form of organizing data such that anyone reviewing it can immediately see patterns, trends, and outliers. For graphs like the one Denise is plotting, each point on the grid corresponds to a data value at a specific time or condition—in this case, weekly data points.

It's imperative when representing data to follow consistent scales and units so that the graphical representation accurately reflects the relationship between variables. Additionally, clarity in labeling each axis with appropriate titles and units eliminates ambiguities, enhancing the data's comprehensibility. Misplacing points can lead to incorrect conclusions or assumptions about the data being represented.

GED Math Practice

Preparing for the General Educational Development (GED) mathematics test involves practicing a variety of topics, including how to use the Cartesian coordinate system effectively. Understanding how to plot data correctly and analyze graphs is an essential skill. The exercise involving Denise's plot is an example of the type of problem-solving scenario one can expect on the test.

Consistent practice in identifying coordinates and graphing them helps reinforce the correct approach. For GED preparation, familiarizing yourself with different types of graphs such as line plots, bar graphs, and scatter plots is crucial. This not only aids in solving math problems but also develops your ability to interpret graphical information, which is a key component of quantitative literacy.