For example, when point P with coordinates (5,4) is reflecting across the X axis and mapped onto point P’, the coordinates of P’ are (5,-4). It might be helpful to talk through an example. Of the 35,086 students who participated, 17,169 or 49% were in 10th grade, 9,928 or 28% were in 9th grade, and the remainder were below than 9th grade. Now, lets reflect Image A in the diagram below across the following lines and write the notation for each reflection: Figure 8.14.5. The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same. That means that the y-values would stay the same, but the x-values will flip. A reflection over the x-axis can be seen in the picture below in which point A is reflected to its image A'. The responses to multiple choice answers for the problem had the following distribution: Choice This task was adapted from problem #3 on the 2012 American Mathematics Competition (AMC) 10B Test. Moreover, reflections of lines, line segments, and angles are all found by reflecting individual points. Reflect over the x-axis: When you reflect a point across the x -axis, the x- coordinate remains the same, but the y -coordinate is transformed into its opposite (its sign is changed). A good picture requires a careful choice of the appropriate region in the plane and the corresponding labels. If the line of reflection was something else (like x -4), you would. If students try to plot this point and the line of reflection on the usual $x$-$y$ coordinate grid, then either the graph will be too big or else the point will lie so close to the line of reflection that it is not clear whether or not it lies on this line. To reflect Triangle ABC across the y-axis, we need to take the negative of the x-value but leave the y-value alone, like this: A (-2, 6) B (-5, 7) C (-4, 4) Please note that the process is a bit simpler than in the video because the line of reflection is the actual y-axis. This is because the coordinates of the point $(1000,2012)$ are very large. Although this problem only applies a reflection to a single point, it has high cognitive demand if the students are prompted to supply a picture. The triangle is located directly on top of the y-axis, so part of the triangle is on one side of the y-axis and part of. The standard 8.G.1 asks students to apply rigid motions to lines, line segments, and angles. This video shows how to reflect a triangle over the y-axis. The purpose of this task is for students to apply a reflection to a single point.
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