Coordinate Algebra Unit 5, Lesson 2 Reflections in the Coordinate Plane

Remember that a reflection is a transformation where a mirror image is created. This is sometimes referred to as a “flip”. A few common reflections occur when points or figures are reflected across the x-axis, the y- axis, or the line y = x.

1)The following diagram shows a reflection across the x-axis. ( ) A B B’ A’ C C’

A)What are the 3 ordered pairs of the preimage, ? ____________________ B) What are the 3 ordered pairs of the image, ? ____________________________ C) How were the values of x and y affected? ______________________________________ D) What is the distance between point C and the line of reflection? _____________ What is the distance between point C’ and the line of reflection? ________________ E) Is this relationship true for points A, A’ and B, B’? ________________________

To indicate a reflection across the x-axis, the notation can be used. Another way to indicate this transformation is to use the notation T(x, y) = (x, -y). This indicates that a transformation occurs where we take the opposite sign on the y-value.

2) Notice that a reflection across the y-axis is similar.( ) A B B’ A’ C C’

A)How were the x and y values affected? ______________________________________ To indicate a reflection across the y-axis, the notation can be used. Another way to indicate this transformation is T(x, y) = (-x, y). This indicates that a transformation occurs where we take the opposite sign on the x- value.

2) A reflection across the line y = x is a little bit different. Note the dashed line representing y = x. A B B’ A’ C C’

A) How were the values of x and y affected? ______________________________________ B) What is the approximate distance between point B and the line of reflection? __________ What is the approximate distance between point B’ and the line of reflection? __________ C) Is this relationship true for points A, A’ and C, C’? ________________________

To indicate a reflection across the line y = x, the notation may be used. Another way to indicate this transformation is T(x, y) = (y, x). This indicates a transformation in which x becomes y and y becomes x. Reflections can occur through other lines, but these are the 3 that are the most common.

1.What does the notation mean? ______________________________________ What does the notation mean? ______________________________________ What does mean? ______________________________________ 2. Given the rule f(x) = (-x, y), what is f(2, 7)? ________ Describe in words what kind of transformation has occurred. ____________________________________

3. Given the point (3, -4) and a transformation by, what is the ordered pair of the image? __________________ 4. a) If a triangle is formed by the points A(2, 6), B(3, 3), and C(6, 5), give the ordered pairs of the image after a transformation of. ______________________ b) How could we describe the transformation using function notation? ________________________

5. If a trapezoid is formed by the points A(4, 2), B(3, 0), C(6, 2), and D(7, 0) and the ordered pairs after a reflection are given by A’(2, 4), B’(0, 3), C’(2, 6), and D’(0, 7), describe the rule for the transformation that occurred using appropriate mathematical notation. _____________________________________________ 6. The point (-4, 5) is reflected across the x-axis. Give the ordered pair for the image. _________________

7) The graph below shows a transformation of. Describe the transformation that has occurred. A BB’ A’ C C’

8) Graph the triangle with vertices A(1, 3), B(2, 6) and C(-3, 5). Then, graph the image that results from the transformation.