![]() Here are a couple of examples to show you how these rules work. The new set of vertices will correspond to the vertices of the reflected image. When reflecting over the line \(y = -x\), besides swaping the places of the x-coordinates and the y-coordinates of the vertices of the original shape, you also need to change their sign, by multiplying them by \(-1\). Step 1: When reflecting over the line \(y = x\), swap the places of the x-coordinates and the y-coordinates of the vertices of the original shape. The steps to follow to perform a reflection over the lines \(y = x\) and \(y = -x\) are as follows: In this case, the x-coordinates and the y-coordinates besides swapping places, they also change sign. The x-coordinates and the y-coordinates of the vertices that form part of the shape swap places. The rules for reflecting over the lines \(y = x\) or \(y = -x\) are shown in the table below: Type of Reflection Step 3: Draw both shapes by joining their corresponding vertices together with straight lines. Step 2: Plot the vertices of the original and reflected images on the coordinate plane. Step 1: Following the reflection rule for this case, change the sign of the x-coordinates of each vertex of the shape, by multiplying them by \(-1\). The steps to follow to perform a reflection over the y-axis are as pretty much the same as the steps for reflection over the x-axis, but the difference is based of the on the change in the reflection rule. The y-coordinates of the vertices will remain the same.The x-coordinates of the vertices that form part of the shape will change sign.Transformations, and there are rules that transformations follow in coordinate geometry.The rule for reflecting over the y-axis is as follows: Type of Reflection In summary, a geometric transformation is how a shape moves on a plane or grid. If you have an isosceles triangle preimage with legs of 9 feet, and you apply a scale factor of 2 3 \frac 3 2 , the image will have legs of 6 feet. Mathematically, a shear looks like this, where m is the shear factor you wish to apply:ĭilating a polygon means repeating the original angles of a polygon and multiplying or dividing every side by a scale factor. Italic letters on a computer are examples of shear. Shearing a figure means fixing one line of the polygon and moving all the other points and lines in a particular direction, in proportion to their distance from the given, fixed-line. If the figure has a vertex at (-5, 4) and you are using the y-axis as the line of reflection, then the reflected vertex will be at (5, 4). Reflecting a polygon across a line of reflection means counting the distance of each vertex to the line, then counting that same distance away from the line in the other direction. ![]() To rotate 270°: (x, y)→ (y, −x) (multiply the x-value times -1 and switch the x- and y-values) ![]() To rotate 180°: (x, y)→(−x, −y) make(multiply both the y-value and x-value times -1) To rotate 90°: (x, y)→(−y, x) (multiply the y-value times -1 and switch the x- and y-values) Rotation using the coordinate grid is similarly easy using the x-axis and y-axis:
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