Reflection in Mathematics

Reflection in mathematics is the transformation of a figure where it is flipped over a line. The line over which the figure is flipped is called the line of reflection. When a figure is reflected, every point on the original figure has a corresponding point on the reflected figure that is the same distance from the line of reflection, but on the opposite side.

Reflection of a Point

When reflecting a point across a line, the distance of the point from the line of reflection remains the same. The new position of the point is determined by drawing a line from the original point to the line of reflection, and then extending the same distance on the opposite side of the line.

Reflection of a Figure

When reflecting a figure across a line, each individual point of the figure is reflected as described above. This results in a mirror image of the original figure across the line of reflection.

Study Guide

Here are the key concepts to understand when studying reflection in mathematics:

Line of Reflection: Understand what the line of reflection is and how it relates to the process of reflection.
Distance: Recognize that the distance of a point from the line of reflection remains the same after reflection.
Mirror Image: Understand that reflection results in a mirror image of the original figure across the line of reflection.
Coordinates: Be able to apply the concept of reflection to points and figures on the coordinate plane.
Properties: Understand the properties of reflected figures, such as congruence and orientation.

Practice applying reflection to various figures and shapes on the coordinate plane, and make sure to understand the geometric reasoning behind the process of reflection.

By mastering the concept of reflection, you will be able to understand how shapes and figures can be transformed and manipulated in the field of mathematics.

◂Math Worksheets and Study Guides Eighth Grade. Displaying data

Organizing & Displaying Data

The resources above cover the following skills:

Data Analysis and Probability (NCTM)

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.

Select and use appropriate statistical methods to analyze data.

Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots.

Develop and evaluate inferences and predictions that are based on data.

Make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit.

Grade 8 Curriculum Focal Points (NCTM)

Data Analysis and Number and Operations and Algebra: Analyzing and summarizing data sets

Students use descriptive statistics, including mean, median, and range, to summarize and compare data sets, and they organize and display data to pose and answer questions. They compare the information provided by the mean and the median and investigate the different effects that changes in data values have on these measures of center. They understand that a measure of center alone does not thoroughly describe a data set because very different data sets can share the same measure of center. Students select the mean or the median as the appropriate measure of center for a given purpose.

Connections to the Grade 8 Focal Points (NCTM)

Data Analysis: Building on their work in previous grades to organize and display data to pose and answer questions, students now see numerical data as an aggregate, which they can often summarize with one or several numbers. In addition to the median, students determine the 25th and 75th percentiles (1st and 3rd quartiles) to obtain information about the spread of data. They may use box-and-whisker plots to convey this information. Students make scatterplots to display bivariate data, and they informally estimate lines of best fit to make and test conjectures.