When reflecting coordinate points of the preimage over the line, the following notation can be used to determine the coordinate points of the image r y=x =(y,x) For example For triangle ABC with coordinate points A(3,3), B(2,1), and C(6,2), apply a reflection over the line y=x By following the notation, we would swap the xvalue and the yvalueIf (a, b) is reflected on the line y = x, its image is the point (b, a) If (a, b) is reflected on the line y = x, its image is the point (b, a) Geometry Reflection A reflection is an isometry, which means the original and image are congruent, that can be described as a "flip"What is the rule for a reflection across the y = x line?
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Reflection over the line y x rule
Reflection over the line y x rule-Reflection 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 (2hThe Lesson A shape can be reflected in the line y = −x If point on a shape is reflected in the line y = −x both coordinates change sign (the coordinate becomes negative if it is positive and vice versa) the xcoordinate becomes the ycoordinate and the ycoordinate becomes the xcoordinate The image below shows a point on a shape being reflected in the line y = −x
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Apply 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 the distance of the xvalue of point A to the line of reflectionFor example, if we are going to make reflection transformation of the point (2,3) about xaxis, after transformation, the point would be (2,3) Here the rule we have applied is (x, y) > (x, y) So we get (2,3) > (2,3) Let us consider the following example to have better understanding of reflectionChange the sign of x coordinates retain y coordinates Hence, the location of reflected point is (1, 2) Plotting the above points in graphical image In the above image;
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)A reflection across the line y = x switches the x and ycoordinates of all the points in a figure such that (x, y) becomes (y, x) Triangle ABC is reflected across the line y = x to form triangle DEF Triangle ABC has vertices A (2, 2), B (6, 5) and C (3, 6)👉 Learn how to reflect points and a figure over a line of symmetry Sometimes the line of symmetry will be a random line or it can be represented by the x
If the line of reflection is y = √(3)x – 4, then m = √(3), θ = Tan1(√(3) ) = 600 and b = 4 Sin(2θ) = , Sin(2θ) = , Cos(2θ) = 05, bSin(2θ) = , and 2bCos 2 (θ) = 2A 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 $$ y = x $$ $ (A,B) \rightarrow (\red B, \red A ) $The rule for a reflection in the line y = x is ( x , y ) → ( y , x ) Reflection in the line y = − x A reflection of a point over the line y = − x is shown
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Original Point ( 1, 2 ) Y axis line is the mirror lineWhen the point is reflected along y axis, follow the below rules;Remember this is a negative diagonal line through the origin answer choices (x, y) becomes (x, y) (x, y) becomes (x, y) Reflect over line y = x Reflect over line y = x answer explanation s Topics Report an issue Quizzes you may like 10 Qs
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Reflection Across the y axis (x,y)>(x, y) Reflection across the line y = x (x,y)>(y, x) Reflection across the line y = x (x,y)>(y,x) 90˚ counterclockwise rotation about the origin (x,y)>(y, x) 180˚ rotation about the originTerms in this set (33) Rule for reflection over the Yaxis (x,y) > (x,y) (reflection) Rule for reflection over the Xaxis (x,y) > (x,y) don't flip, take OPPOSITE of 2nd (take OPPOSITE, don't just make it neg) (reflection) Rule for reflection over the Y=X line (x,y) > (y,x) Flip (reflection) X
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