The New York State Next Generation Mathematics Learning Standards (2017) reflect revisions, additions, vertical movement, and clarifications to the current mathematics standards. These revised standards reflect the collaborative efforts and expertise of all constituents involved. Through numerous phases of public comment, virtual and face-to-face meetings with committees consisting of NYS educators (Special Education, Bilingual Education and English as a New Language teachers), parents, curriculum specialists, school administrators, college professors, and experts in cognitive research, the New York State Next Generation Mathematics Learning Standards (2017) were developed. In 2015, New York State (NYS) began a process of review and revision of its current mathematics standards adopted in January of 2011. Religious and Independent School Support.New York State Alternate Assessment (NYSAA).Teaching in Remote/Hybrid Learning Environments (TRLE).Next Generation Learning Standards: ELA and Math.When reflecting a shape over the line \(y = -x\), swap the places of the x-coordinates and the y-coordinates of the vertices of the original shape, and change their sign, to obtain the vertices of the reflected image.When reflecting a shape over the line \(y = x\), swap the places of the x-coordinates and the y-coordinates of the vertices of the original shape, to obtain the vertices of the reflected image.When reflecting a shape over the y-axis, change the sign of the x-coordinates of each vertex of the original shape, to obtain the vertices of the reflected image.When reflecting a shape over the x-axis, change the sign of the y-coordinates of each vertex of the original shape, to obtain the vertices of the reflected image.The original shape being reflected is called the pre-image, whilst the reflected shape is known as the reflected image.The line is called the line of reflection. In Geometry, reflection is a transformation where each point in a shape is moved an equal distance across a given line.Now that we have explored each reflection case separately, let's summarize the formulas of the rules that you need to keep in mind when reflecting shapes on the coordinate plane: Type of Reflection Reflection over the line \(y = -x\) example Reflection Formulas in Coordinate Geometry \ Steps 2 and 3: Plot the vertices of the original and reflected images on the coordinate plane, and draw both shapes.įig. Step 1: The reflection is over the line \(y = -x\), therefore, you need to swap the places of the x-coordinates and the y-coordinates of the vertices of the original shape, and change their sign, to obtain the vertices of the reflected image. 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.The rule for reflecting over the y-axis is as follows: Type of Reflection
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