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Quiz & Worksheet Goals In these assessments, you'll be tested on The rules that govern reflections across both the x and y axes individually Identifying y=x reflections Identifying reflections The rule for reflecting over the X axis is to negate the value of the ycoordinate of each point, but leave the xvalue the same 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)To reflect a figure across a line of reflection, reflect each of its vertices Then connect the vertices to form the image Each point and its image must be at the same distance from the line of reflection We can use the rules shown in the table for changing the signs of the coordinates after a reflection

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Reflection across y=x rule-Glide Reflection A glide reflection is a composition of transformations In a glide reflection, a translation is first performed on the figure, then it is reflected over a line Therefore, the only required information is the translation rule and a line to reflect over A common example of glide reflections is footsteps in the sandA reflection of a point over the x axis is shown The rule for a reflection over the x axis is (x, y) → (x, − y) Reflection in the y axis A reflection of a point over the y axis is shown

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Kite abcd is reflected over the line y = x what rule shows the input and output of the reflection, and what is the new coordinate of a'?Click and drag the blue dot and watch it's reflection across the line y=x (the green dot) Pay attention to the coordinates How do they relate to each other?Reflections and Rotations We can also reflect the graph of a function over the xaxis (y = 0), the yaxis(x = 0), or the line y = x Making the output negative reflects the graph over the xaxis, or the line y = 0 Here are the graphs of y = f (x) and y = f (x)

REFLECTIONS Reflections are a flip The flip is performed over the "line of reflection" Lines of symmetry are examples of lines of reflection Reflections are isometric, but do not preserve orientation Coordinate plane rules Over the xaxis (x, y) (x, –y) Over the yaxis (x, y) (–x, y)14 Reflections Over y = x, y = –x, y = #, & x = # Geometry Directions Write the rule of the transformation (This is a mixed review) 1) A line segment is reflected over y = –x 2) A line segment is translated 5 units left & 1 unit up 3) A triangle is reflected over x = 0 4) A triangle is reflected over y = xAnswer choices Reflection across y = −1 Reflection across y = 1 Reflection across x = −1 Reflect over the line y = x answer choices (2, 4) (4, 2) (4, 2) (4, 2) s Question 18 SURVEY 30 seconds Q

The line that represents y=x has a slope of 1/1 If i am considering a point, ill refer to it as A at (4,3) and reflect it over line y=x i will be at (4,3) which i will refer to as point B I can prove this relationship using simple geometry I wiAnswer choices Reflect over the xaxis, translate (x8,y) Reflect over the xaxis then translate (x6, y) Reflect over the yaxis then (x1, y1) Translate down 4 (y4) and to the right 5 (x5) sReflection Rules STUDY Flashcards Learn Write Spell Test PLAY Match Gravity Created by paigesutula Key Concepts Terms in this set (15) reflect over xaxis (x,y) reflect over yaxis (x,y) reflect over line y=x (y,x) reflect over line y= x (y,x) reflect thru origin (x,y) reflect thru a different point ex (5,1) h=5 k= 1 (2h

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Reflect over the xaxis 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) If you forget the rules for reflections when graphing, simply fold your paper along the x axis (the line of reflection) to see where the new figure will be located The notation or rule for a reflection over the yaxis is (x, y) → (x, y)Step 1 Extend a perpendicular line segment from to the reflection line and measure it Since the reflection line is perfectly horizontal, a line perpendicular to it would be perfectly vertical Created with Raphaël Step 2 Extend the line segment in the same direction and by the same measure Created with Raphaël

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SWBAT reflect an image over y=x On the other hand, the rule of reflection for the point reflected across y = x is, the rule would be, (x, y) > (y, x) So the values would switch places and would have the opposite sign (If the number was positive, it would be a negative, and if it was a negative number, it would turn into a positive) From the diagram we see the object point ( − 2, −5) is mapped to (x',y') by a reflection in the line X = 2 we note (1) the ycoordinate is unaffected (2) for reflections the distance from the line of reflection to the object is equal to the distance to the image point ∴ a = 2 2 = 4units so the image point is 4 units from the line of

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 We have to identify the rules of reflection Firstly, the rule for reflecting a point about the line y=x is While reflecting about the line y=x, we get the reflected points by swapping the coordinates So, Option 3 is correct Now, the rule for reflecting a point about the line y= x isReflection over axis Rule Graph on Graph paper Label the image and pre image 4, Triargle A(2, 2), B(3, 0) Reflection across xaxis Rule Graph on Graph paper Label the image and pre image (Describe the transformation that is represented by the given rule 8 A(x, y) (x y 4) 10 y) (x, y 5) dam 12 (x, y) 9 Q(x, y) (x, y 2) 11 Find out the units up that the point (1, 3) is from the line, y=2 It is one unit up from the line, so go over one unit on the xaxis and drop down one unit The You should graph the regular points and the reflection points It looks good if you can graph the regular points in one color and the reflection ones in a different color

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 Reflection Over y = 2 With Rule by Lance Powell on image/svgxml ShareReflection over y=mxb Adjust the inputs to y=mxb by using the slider, choosing values for m and b Observe the coordinates of the original figure and its reflectionA line segment is reflected over y = –x 3) A triangle is reflected over x = 0 2) A line segment is translated 5 units left & 1 unit up 4) A triangle is reflected over y = x

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Get the free "Reflection Calculator MyALevelMathsTutor" widget for your website, blog, Wordpress, Blogger, or iGoogle Find more Education widgets in WolframAlphaKite abcd is shown a is at negative 7, 2, b is at negative 5, 3, c is at negative 2, 2, d is at negative 5, 1(x,y)→(x,y) Write the rule reflection over the yaxis (x,y)→(y,x) Write the rule 90⁰ counter clockwise rotation (x,y)→(x,y) Write the rule 180⁰ rotation (x,y)→(y,x) Write the rule 270⁰ counter clockwise rotation It means sliding an object into different directions

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The linear transformation rule (p, s) → (r, s) for reflecting a figure over the oblique line y = mx b where r and s are functions of p, q, b, and θ = Tan 1 (m) is shown below Finding the linear transformation rule given the equation of the line of reflection equation y = mx b involves using a calculator to find angle θ = Tan 1 (mCorresponding parts of the figures are the same distance from the line of reflection Ordered pair rules reflect over the xaxis (x, y), yaxis (x, y), line y = x (y, x) This video shows reflection over the xaxis, yaxis, x = 2, y = −2 Show Video Lesson300 seconds Q What is the sequence of transformations for the image given?

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Problem 1 Find a linear transformation rule of the form (p, q) → (r, s) such that the reflection image of the point (p, q) over the oblique line y = mx b is the point (r, s) In the general case, both r and s are functions of p, q, m and bThe Laws of Reflection state !What is the rule for the following reflection?

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This is a KS3 lesson on reflecting a shape in the line y = −x using Cartesian coordinates It is for students from Year 7 who are preparing for GCSE This page includes a lesson covering 'how to reflect a shape in the line y = −x using Cartesian coordinates' as well as a 15question worksheet, which is printable, editable and sendableApply a reflection over the line x=3 Since the line of reflection is no longer the xaxis or the yaxis, we cannot simply negate the x or yvalues This is a different form of the transformation Let's work with point A first Since it will be a horizontal reflection, where the reflection is over x=3, we first need to determine theGeometry reflection A reflection is a "flip" of an object over a line Let's look at two very common reflections a horizontal reflection and a vertical reflection

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For this type of reflection, all you have to do is switch the x and y values if a point is (4,2), then the inverse is (2,4) If you begin with a function y=sqrt (x), there are many different lines you could reflect this function across, but only reflecting over y=xThe incident ray, the reflected ray, and the normal to the surface of the mirror all lie in the same plane Author Ben Gordon This type of activity is known as PracticePlease read the guidance notes here, where you will find useful information for running these types of activities with your students 1 ExampleProblem Pair 2 Intelligent Practice 3 Answers

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A point reflection is just a type of reflection In standard reflections, we reflect over a line, like the yaxis or the xaxisFor a point reflection, we actually reflect over a specific point, usually that point is the origin $ \text{Formula} \\ r_{(origin)} \\ (a,b) \rightarrow ( \red a , \red b) $Reflection about the line y=x Once students understand the rules which they have to apply for reflection transformation, they can easily make reflection transformation of a figure For example, if we are going to make reflection transformation of the point (2,3) about xaxis, after transformation, the point would be (2,3) REFLECTION RULES Worksheet 17 REFLECTION OVER THE Y AXIS PREIMAGE LOCATION REFLECTION IMAGE LOCATION a) Place DEF on the coordinate grid at

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Reflections Date_____ Period____ Graph the image of the figure using the transformation given 1) reflection across y = −2 x y E I Q Z 2) reflection across the xaxis W M D A 3) reflection across y = −x x y J A S T 4) reflection across y = −1 x y B I W L 5) reflection across x = −3 x y P I W S 6) reflection across y = x x y Q H L P1Reflection over the line y = − x A reflection in the line y = x can be seen in the picture below in which A is reflected to its image A' The general rule for a reflection in the y = − x If you reflect over the line y = x, the xcoordinate and ycoordinate change places and are negated (the signs are changed) the line y = x is the point (y, x) Also, what are the two rules of reflection?

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Geometry 3 people liked this ShowMe Flag ShowMe Viewed after searching for reflect over x= 1 reflection over the line y=x Reflection over y=x reflection over yaxis reflectionAnotation rulehas the following formry−axisA→B=ry−axis(x,y)→(−x,y)and tells you that the image Ahas been reflected across theyaxis and thexcoordinates have been multiplied by 1

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