Design your real-world scenario involving a geometric figure and its transformations. Model the pre-image and image on a coordinate plane. In your final answer, include the real-world scenario, written in complete sentences, the transformations that map the pre-image onto its image, and all calculations involved for the equations of the corresponding lines or the coordinates for the corresponding vertices. Also, please include a sketch of the pre-image and the image.
In the United States, the average public school teacher currently earns an annual salary near $55,000. Reported national average salaries for the last six decades are listed below.
Year National
Average
Teachers'
Salary
1960 $4,995
1970 $8,626
1980 $15,970
1990 $31,367
2000 $41,807
2010 $55,202
Use the data represented in the table to answer the following prompts. Answer in complete sentences and include all necessary calculations.
The table used to represent the national average teachers’ salary per decade did not include the data for the year 1950. If the mean national average teachers’ salary per decade for the seven decades is $22,986 per decade, what salary should have been reported for the year 1950? In your final answer, include all of the necessary calculations.
The National Board of Education predicts that the 2020 national census will report the average annual salary of a teacher to be $60,000. Based on the board of education’s prediction, how will the mean, median, and mode of the original data table be affected by the additional data collected in 2020? Note: Do not include data for 1950.
In the United States, the average public school teacher currently earns an annual salary near $55,000. Reported national average salaries for the last six decades are listed below.
Year National
Average
Teachers'
Salary
1960 $4,995
1970 $8,626
1980 $15,970
1990 $31,367
2000 $41,807
2010 $55,202
Create a scatter plot of the data represented in the table of teachers’ salaries. Be sure to include all appropriate labels.
Use the scatter plot created for question #1 to write a line of best fit in the slope-intercept form for the data. In your final answer, include all necessary calculations.
For the equation of the line best fit, predict the national average teachers’ salary for the year 2014. In your final answer, include all necessary calculations.
To determine the best fit undergraduate program, a high school senior researches the majors offered at the universities he is considering for admissions. The internet search reports that Arizona State University lists nine of their most popular majors and the percent of the student population enrolled in the programs.
Popular Majors Percent of Student body
Biology 8%
Business Marketing 20%
Communications/Journalism 6%
Education 5%
Engineering 7%
Interdisciplinary Studies 6%
Psychology 6%
Social Sciences 10%
Visual and Performing Arts 8%
The university’s enrollment is expected to reach at least 22,000 students for the fall semester.
Create a circle graph to represent the university’s expected student enrollment according to major. You may hand draw or use a technology program to create your circle graph.
Create a bar graph to represent the university’s expected student enrollment according to major. You may hand draw or use a technology program to create your bar graph.
Real-World Scenario:
Let's consider the scenario of a kite flying in the sky. A kite is a geometric figure with four sides, a parallelogram shape, and two pairs of congruent adjacent sides. Initially, the kite is flying at coordinates (-2, 3), (-1, 0), (2, 0), and (0, 5).
Transformations:
To transform the pre-image of the kite to its image, we will perform two transformations: a translation and a reflection.
1. Translation:
Let's translate the kite 3 units to the right and 2 units up. This transformation will represent the motion of the kite as it moves with the wind.
To calculate the new coordinates for the translated image, we can add the translation amounts to the corresponding coordinates of the pre-image:
(-2+3, 3+2), (-1+3, 0+2), (2+3, 0+2), and (0+3, 5+2).
The translated image coordinates are: (1, 5), (2, 2), (5, 2), and (3, 7).
2. Reflection:
Next, let's reflect the translated image of the kite across the x-axis. This transformation represents the motion of the kite as it flips in the air due to wind gusts.
To reflect a point over the x-axis, we negate the y-coordinate. Therefore, the new coordinates of the reflected image are:
(1, -5), (2, -2), (5, -2), and (3, -7).
Calculations:
Translation:
Translated Image Points:
(-2+3, 3+2) = (1, 5)
(-1+3, 0+2) = (2, 2)
(2+3, 0+2) = (5, 2)
(0+3, 5+2) = (3, 7)
Reflection:
Reflected Image Points:
(1, 5) reflects to (1, -5)
(2, 2) reflects to (2, -2)
(5, 2) reflects to (5, -2)
(3, 7) reflects to (3, -7)
Sketch:
Please refer to the attached image for the sketch of the pre-image and the image of the kite.
[Attached Image: Pre-image and Image Sketch of the Kite Transformation]
In conclusion, the scenario describes a kite flying in the sky. The pre-image of the kite has coordinates (-2, 3), (-1, 0), (2, 0), and (0, 5). To represent its motion due to wind, we translate the pre-image 3 units to the right and 2 units up, resulting in the translated image coordinates of (1, 5), (2, 2), (5, 2), and (3, 7). Finally, we reflect the translated image across the x-axis, resulting in the reflected image coordinates of (1, -5), (2, -2), (5, -2), and (3, -7).