Midterm

The test has four components. CHOOSE THREE OF THE FOUR TO COMPLETE. Read the instructions for each component carefully. While some components require the use of a computer with access to the internet, you may not access webpages other than the ones linked below and you may not communicate with your peers or anyone else during the test.

1. Geometry component

Answer the questions in the space provided on the paper. (Here’s a link link to the PDF if you’d like to view the paper on the computer.)

2. Written component

Click on this link to access the instructions and linked form. Do not submit until you are happy with your answers.

3. Desmos component

1. Click on this link to access the Desmos activity.
2. Do not sign into your Desmos account; enter your name when asked.
3. Complete the activity by answering the questions on each page. Your work is automatically saved. You will be able to go back and edit your previous answers during the test as long as you keep the browser tab open.

4. GeoGebra component

Complete using the GeoGebra desktop app. Save your response as a GeoGebra (.ggb) file with your name as its filename. Email your file as an attachment to kate.poirier@utoronto.ca. (Save a copy of your file for your records.)

1. Place 6 points A, B, C, D, E, F in the plane so that A, C, and E lie on one line and B, D, and F lie on another line.
2. Color the two lines black and color the 6 points A, B, C, D, E, F gray.
3. Create the lines and and color them red. Let L be their intersection point. Color the point L red.
4. Create the lines and and color them green. Let M be their intersection point. Color the point M green.
5. Create the lines and and color them blue. Let N be their intersection point. Color the point N blue.
6. Use the drag test to see how the configuration of lines and points changes as you move the free points around. Pay special attention to the points L, M, and N.
7. Make a conjecture about the relationship between the points L, M, and N. (Hint, it may be helpful to hide all the lines and perform the drag test again.) Create one text box containing the statement of your conjecture. Be explicit and precise. Use full sentences.
8. Does the drag test consist of a proof of your conjecture? Why or why not? Create a second text box containing your answer.