Probably it’s best to do this graphically then get the coordinates from it. The reflection of triangle will look like this. Point is units from the line so we go units to the right and we end up with. Is units away so we’re going to move units horizontally and we get. Formula, Examples, Practice and Interactive Applet on common types of reflections like x-axis, y-axis and lines: Home Transformations Reflections Reflect a Point Across x axis, y axis and other lines A reflection is a kind of transformation. Consider reflecting every point about the 45 degree line y x. Point is units from the line, so we’re going units to the right of it. The second transformation is reflection which is similar to mirroring images. 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. A line rather than the -axis or the -axis. 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. I am completely new to linear algebra so I have absolutely no idea how to go about deriving the formula. 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 linear transformation matrix for a reflection across the line y m x is: 1 1 + m 2 ( 1 m 2 2 m 2 m m 2 1) My professor gave us the formula above with no explanation why it works. 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. 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.
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