What are the coordinates of points under reflection?

mirror image

In Activity 1 you learned about the meaning of the coordinates of points on an x-y coordinate system, also called Cartesian coordinate system.

In this activity, you will learn how the points in the Cartesian plane are related. By the end of this activity you should be able predict the location of points in the quadrants as well as the coordinates of points which are reflections of each other along the x-axis and the y-axis. You will also learn in this activity how to use the “Reflect” tool of GeoGebra.

Activity 2
1. If you put a mirror along the y-axis, locate the reflections of the points A, B, C, D, E, F on the right side of the y-axis. Use the point tool [.A] to plot the points.

2. What do you notice about the coordinates of the set of points A, B, C, D, and E? How do their coordinates compare with the coordinates of their reflections?

3. Reflect the points along the x-axis using the ‘reflect’ tool [.\.], the button to the right of the point tool. To do this click the reflect tool then click the point you want to reflect then click the x-axis, the line of reflection. (Click this link to check if you have the correct location of points.)

4. The x and y axes divide the plane into four quadrants. What can you generalize about the signs of the coordinates of the points in each of the quadrants? You can verify your generalization by plotting the points. For example, predict which quadrants point P(-5,4) will be then in the input bar type P=(-5,4).

5. What can you generalize about the coordinates of points which are reflections of each other along the y– axis? x-axis?

Discuss you answers to this Activity with your seatmate. If you have questions you cannot settle, ask you teacher. When you are ready proceed to Activity 3.