What is a reflection? A reflection is a mirror image of the original figure. It is the result of a transformation of a figure over a line called the line of reflection. *In a reflection, each point of the preimage and its image are the same distance from the line of reflection.* 1 Take point (-2, 5) and reflect it across the y-axis. Take point (-2, 5) and reflect it across the x-axis. What do you notice about the coordinates of the image points? 2 When reflecting a point over the x-axis, which coordinate remains the same? If point A is 2 units above the x-axis, what will be the y-coordinate of the reflected point? If point B is three units above the x-axis, what will be the y-coordinate of the reflected point? If point C is one unit below the x-axis, what will be the y-coordinate of the reflected point? 3 When reflecting a point over the y-axis, which coordinate remains the same? If point K is two units to the right of the y-axis, what will be the x-coordinate of the reflected point? If point L is five units to the right of the y-axis, what will be the x-coordinate of the reflected point? If point M is four units to the left of the y-axis, what will be the x-coordinate of the reflected point? 4 Triange ABC has vertices A(5, 2), B(1,3), and C(-1,1). Graph the figure and its reflected image over the x-axis. Find the coordinates of the vertices of the reflected image. 5 Whiteboards: Quadrilateral KLMN has vertices K(2, 3) L(5, 1) M(4, -2) N(1, -1) Graph the figure and its reflection over the y-axis. Then find the coordinates of the vertices of the reflected image. 6 Whiteboards: Triange PQR has vertices P(1, 4) Q(3, 7) R(4, -1) Graph the figure and its reflection over the x-axis. Then find the coordinates of the vertices of the reflected image. 7 How can you determine the coordinates of a figure after a reflection over the x-axis? How can you determine the coordinates of a figure after a reflection over the y-axis? 8 Your friend is finding the coordinates of the image of a triangle with vertices A(1, 1), B(4, 1) and C(1, 5) after a reflection over the x-axis. He says the new coordinates are Al(-1, 1), Bl(-4, 1) and Cl(-1,5). Is he right? Why or why not? 9 Try this: Suppose you reflect a triangle in Quadrant I over the y-axis, then translate the image 2 units left and 3 units down. Is there a single transformation that maps the preimage onto the image? Explain 10 What transformation occurred? A(-2, 5) A'(2, 5) B(4, -9) B'(4, 9) What about this one? C(3, -5) C'(-3, 5) 11
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