Probably it’s best to do this graphically then get the coordinates from it. So let’s get started A transformation that uses a line that acts as a mirror, with an original figure ( preimage) reflected in the line to create a new figure ( image) is called a reflection. The reflection of triangle will look like this. You’re going to learn how to find the line of reflection, graph a reflection in a coordinate plane, and so much more. Reflections in the x-axis If (f (x) x2), then (-f (x) - (x2)). Point is units from the line so we go units to the right and we end up with. Reflections of graphs Graphs can be reflected in either the (x) or (y) axes. Is units away so we’re going to move units horizontally and we get. Point is units from the line, so we’re going units to the right of it. We’re just going to treat it like we are doing reflecting over the -axis. Graphically, this is the same as reflecting over the -axis. This line is called because anywhere on this line and it doesn’t matter what the value is. It can also be defined as the inversion through a. A line rather than the -axis or the -axis. Point reflection, also called as an inversion in a point is defined as an isometry of Euclidean space. Let’s say we want to reflect this triangle over this line. The procedure to determine the coordinate points of the image are the same as that of the previous example with minor differences that the change will be applied to the y-value and the x-value stays the same. In the end, we found out that after a reflection over the line x=-3, the coordinate points of the image are:Ī'(0,1), B'(-1,5), and C'(-1, 2) Vertical Reflection The y-value will not be changing, so the coordinate point for point A’ would be (0, 1) Since point A is located three units from the line of reflection, we would find the point three units from the line of reflection from the other side. It is common to observe this law at work in a Physics lab such as the one described in the previous part of Lesson 1. We’ll be using the absolute value to determine the distance. Since it will be a horizontal reflection, where the reflection is over x=-3, we first need to determine the distance of the x-value of point A to the line of reflection. This is a different form of the transformation. Since the line of reflection is no longer the x-axis or the y-axis, we cannot simply negate the x- or y-values. Reflection across the \(x\)-axis.Let’s use triangle ABC with points A(-6,1), B(-5,5), and C(-5,2). Graph the image of the figure using the transformation given. ![]() There is also an extension where students try to reflect a pre-image across the line y x. When reflecting a point in the origin, both the \(x\)-coordinate and the \(y\)-coordinate is negated.\((x, y)→(-x, -y)\) In this activity, students explore reflections over the x-axis and y-axis, with an emphasis on how the coordinates of the pre-image and image are related. ![]()
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