Reflections across f(x) = x
Directions
Points C, D, and E are graped above. [br]The line [math]f\left(x\right)=x[/math] or [math]y=x[/math] is graphed aboved.[br]Reflect points C,D, & E over the line.[br]1) Click on the "reflection about line" tool[br]2) Click on the line of reflection then[br]3) Click on the point you want to reflect[br]These steps should plot the pre-images C', D' and E'.
Observation
What do you notice about the pre-image and image coordinates?[br]Based on your observations, write a rule describing how the coordinates change when reflected over the line [math]f\left(x\right)=x[/math].
PRACTICE: f(x) = x reflections
Use the graph below to answer the questions that follow.
Question 1
Triangle ABC has vertices located at A(9, 0) B(4, 1) C(5, 3)[br]What are the vertices of Triangle A'B'C' given a reflection across the line f(x) = x?
Question 2
Rectangle WXYZ has vertices located at W(0, 0) X(5, 0) Y(5, 5) Z(0, 5)[br]What are the vertices of Rectangle W'X'Y'Z given a reflection across the line f(x) = x?