Reflecting in the line y = x

Part A

When you take a point such as (3, 5) or (-2, 8) or any other such point and reflect in the line with equation y = x, what happens..? In the diagram below there are four points A, B, C and D. Using the applet reflect these points in the line shown, the line y = x.

Question 1

What do you notice about the coordinates of the IMAGES of A, B, C and D under reflection in the line y = x?

Part B

In the applet below the point A lies on the graph of the function

, and the black line is the line y = x. With Trace Off change the value of the slider to move the position of point A.

Question 2

What is the relationship between points A and A' ?

Question 3

With Trace On, again using the slider, change the position of point A. What do you notice about the line traced out by A' ?

Question 4

In the space below, write the equation of the line traced out by A' as point A moves.

Part C

The applet below shows the line y = x (the blue broken line), and the graph of the function

. The point A lines on the line with equation

Question 5

Find the equation of the red line in the form

Question 6

With Trace off, drag the point A. What is the relationship between A and A' ?

Question 7

Turn Trace on and now again, drag the point A. What is the equation of the line traced out by A' ?

Question 8

Using the graph below, find equations in the form for both; i. the red line ii. the trace line

Part D

The applet below shows the line y = x (the broken line), and the graph of the function

Question 9

With the trace off, drag the point A. What is the relationship between point A and A' ?

Question 10

Turn the Trace on and drag point A again. What is the equation of the line traced out by the point A' ?