Slide, Flip, and Turn

Slide, Flip, and Turn

Reflections

Today, we are going to use Geometer’s Sketchpad to explore what happens to the coordinates of points when they are reflected over the y-axis and the x-axis.

Part I

First, we need to construct our axes. Go to the top of the screen and under Graph, you will choose Show Grid.

To construct a point anywhere on your graph, click on the point icon (the little dot) at the left of the screen. Then put the point anywhere that you would like on your grid and click again. We want to label this point, so go to the top of the screen under Measure and select Coordinates. (Notice that the computer labels this point A.)

What are the coordinates of point A? ______

Next, we are going to reflect this point over the y-axis. Click on the top icon at the left of your screen. (This is the selection arrow.) Now select the y-axis by clicking on it. Then go to the top of the screen to Transform and move down to Mark Mirror. You should see the y-axis blink. This signifies that it is your mirror. Now select your point by clicking on it. Next, go to Transform and Reflect. You should see a new point. Now go to Measure and select Coordinates again. (Notice that the computer labels this point A’.)

What are the coordinates of point A’? ______

Now pick five more points anywhere on your graph and reflect them over the y-axis. List the coordinates of the original point and its reflection below.

1.) Point ______Reflected Point ______

2.) Point ______Reflected Point ______

3.) Point ______Reflected Point ______

4.) Point ______Reflected Point ______

5.) Point ______Reflected Point ______

Fill in the blank to generalize what happens to the coordinates of each point when it is reflected over the y-axis?

The ______-coordinate changes to its ______, while the

______-coordinate remains the same.

Part II

Now we are going to take a point and reflect it over the x-axis. We will use the same process as above. If you would like to start with a fresh graph, go to File and select New Sketch. Don’t forget to add your grid.

Make a new point. The coordinates of your point are ______.

Start again, but choose the x-axis as your mirror. (Please read the previous instructions if you have forgotten how to do this.) Reflect your point over the x-axis.

What are the coordinates of your new point? ______

Choose five more points and reflect them. What are the coordinates of each?

1.) Point ______Reflected Point ______

2.) Point ______Reflected Point ______

3.) Point ______Reflected Point ______

4.) Point ______Reflected Point ______

5.) Point ______Reflected Point ______

Make a generalization about any point that is reflected over the x-axis.

Part III

Finally, we are going to reflect a triangle over the y-axis. As always, first go to Graph and Show Grid. Next, use the point tool (the dot) and click three times to make three different points on the grid.

Next, click on the selection arrow. While you hold down the Shift key, click on the other two points that are not marked (selected). Now you may go to Measure and Coordinates. This will label and measure all three points at the same time.

Click on the y-axis and go to Transform->Mark Mirror.

Use the shift key to again mark all three points at the same time. Go to the Transform menu and choose Reflect. Finally, go to Measure->Coordinates.

List the coordinates of the original points and their reflections in the space below.

A ______A’ ______

B ______B’ ______

C ______C’ ______

Now that we have all of the points, let’s make the two triangles. First, hold the Shift key and select points A, B, and C. Then go up to the Construct menu and choose Triangle Interior. (Notice that the triangle is criss-crossed. This means that it is selected. Click on the triangle once again to de-select it.)

Next, select points A’, B’, and C’ and construct another triangle interior.

Once you have constructed both triangles, click on one and move it around. What happens to the other triangle?

Homework: For homework tonight, I would like you to draw your own triangle on the graph paper that I will be providing. Then reflect your triangle over the

x-axis. List the coordinates of points A, B, and C, as well as points A’, B’, and C’. I will be collecting your graphs and these notes in class tomorrow.