Reflections in the Coordinate Plane

Name ______

In this activity, you’ll investigate what happens to the coordinates of points when you reflect them across the x- and y-axis in the coordinate plane.

1. Chose Show Grid from the Graph menu.

2. Draw triangle CDE in the first quadrant with vertices on the grid. In order to do this, chose Snap Points from the Graph menu.

3. Measure the coordinates of each vertex.

4. Mark the y-axis as a mirror.

5. Reflect the triangle across the y-axis by selecting the whole triangle and choosing Reflect from the Transform menu. Your sketch should know look like the following:

C: (1.01, 1.01) D D' 4 D: (2.99, 4.00)

E: (5.00, 2.01)

E' 2 E C C'

6. Measure the coordinates of the image’s vertices.

7. Drag the vertices to different points on the grid and look for a relationship between a point’s coordinates and the coordinates of the reflected image across the y-axis. Question 1: Describe any relationship you observe between the coordinates of the vertices of your original triangle and the coordinates of their reflected images across the y-axis.

______

8. Now mark the x-axis as a mirror and reflect your original triangle across the x-axis.

9. Before you measure the coordinates of this image, predict what they will be. Then measure to confirm your prediction.

Prediction: ______

Question 2: Describe any relationship you observe between the coordinates of the vertices of your original triangle and the coordinates of their reflected images across the x-axis.

______

10. Start a new sketch and redo steps 1-3.

11. Draw the line y=x on the grid. Try to do this on your own. Write down the steps that you tried. If you must, read the hint at the bottom of the last page. However, you must TRY something in order to read the hint.

Write the steps that you tried below. Check with me when you are finished.

______

12. Mark the line y=x as a mirror.

13. Reflect the triangle across the line y=x by selecting the whole triangle and choosing Reflect from the Transform menu. 14. Before you measure the coordinates of this image, predict what they will be. Then measure to confirm your prediction.

Prediction: ______

Question 3: Describe any relationship you observe between the coordinates of the vertices of your original triangle and the coordinates of their reflected images across the line y = x.

______

Summary: Use the following chart to summarize your results:

Original Triangle (x, y)

Triangle Reflected across the x-axis Triangle Reflected across the y-axis Triangle Reflected across the line y=x

Hint: Use your point tool to create a point at (1, 1). Then select this point and the origin and choose Line from the construct menu. Name ______

Translations in the Coordinate Plane

In this activity, you’ll investigate what happens to the coordinates of points when they are translated in the coordinate plane.

1. Chose Show Grid from the Graph menu.

2. Chose Snap Points from the Graph menu.

3. Draw a segment from the origin to anywhere on the grid. Label the endpoint C.

3. Measure the coordinates of point C only.

4. Mark the vector that you just constructed. TO do this, chose both ends of the vector and chose Mark Vector from the Transform menu.

5. Draw triangle DEF with vertices on the grid in the first quadrant. Measure the vertices.

6. Translate the triangle by the marked vector. (Select the triangle and choose Translate under the construct menu. Make sure Marked is selected).

7. Measure the coordinates of the image’s vertices.

8. Experiment by dragging point C or any of the triangles vertices. Look for a relationship between a point’s coordinates and the coordinates of its image under a translation.

Question 1: Where can you drag point C so that the original points and the corresponding image points always have the same y-coordinates but different x-coordinates? ______

Question 2: Where can you drag point C so that the original point and the corresponding image points always have the same x-coordinates but different y-coordinates? ______Question 3: When the vector defined by the origin and point C translates your original triangle to the left and up, what must be true of the coordinates of point C? ______

Question 4: Move the endpoint, C, of the vector to point (2, 1). How are the point D and D' related? How are the point E and E' related? How are the point F and F' related? ______

Question 5: Move the endpoint, C, of the vector to point (1, 3). How are the point D and D' related? How are the point E and E' related? How are the point F and F' related?

______

Question 6: Summary Statement- Suppose point C has coordinates (x, y). What are the coordinates of the image of a point under translation by (a, b)?

______Name ______

Rotations in the Coordinate Plane

In this activity, you will investigate what happens to the coordinates of points when they are rotated in the coordinate plane about the origin.

1. Show the grid.

2. Mark the origin as a center of rotation by selecting the origin and choosing Mark Center from the transform menu.

3. Draw triangle CDE with vertices on the grid in the first quadrant. In order to do this, chose Snap Points from the Graph menu.

4. Measure the coordinates of each vertex.

5. Select the triangle and rotate it 90°. Measure the coordinates of the image.

Question 1: Describe any relationship you observe between the coordinates of the vertices of your original triangle and the coordinates of the images rotated 90° about the origin.

______

6. Rotate the original triangle 180° about the origin.

Prediction: ______

______8. Rotate the original triangle 270° about the origin.

Prediction: ______

______

Question 4: If you rotate the original triangle 360º about the origin, where will it end up? How do you know? ______

Summary: Use the following chart to summarize your results:

Original Triangle (x, y)

Triangle Rotated 90º about origin Triangle Rotated 180º about origin Triangle Rotated 270º about origin