Coordinate AlgebraUnit 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. ( )''' CBAABC

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’? ________________________

ABC

''' CBA

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.

axisxr

2) Notice that a reflection across the y-axis is similar.( )''' CBAABC

A BB’ A’

CC’

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.

axisyr

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

''' CBAABC

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.

xyr

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. ____________________________________

axisxr

axisyr

1yr

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? ________________________

1,5T

axisxr

axisxr

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.

''' CBAABC

A

BB’

A’

CC’

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 .xyr